----~ -~ olce Que stio ns (with One Corre ct Anew

I I, SHM and Its characteristics I (Mole wt. of silvcr = 108 and Avagadro nwner
= 6.02 x 1023 gm mole-1)
1. The displacement of a particle executing simple
harmonic motion is given by; (a) 6.4 Nim (b) 7.1 Nim
y = A 0 + A sin mt•+ B cos rot (c) 2.2 Nim (d) 5.5 N/m
Then the amplitude of its oscillation is given by: (JEE Main 2018)
4. A particle performs harmonic oscillations along
(a) Ao + .JA 2 + B2 a straight line with a period of 6 s and amplitude
4 cm. The mean velocity of the particle averaged
over the time interval during which it travels a
(c) ✓AJ +(A+ B) 2 (d)A +B distance of 2 cm startin g from the extrem e
(NEET 2019) position is
2. A particl e is executing SHM along a straight line. (a) 1 cm s-1 (b) 2 cm s-1
Its velocities at distances X1 and,½ fro~ the m~an (c) 4 cm s-1 (d) 8 cm s-1.
positio n are v 1 and V2 respectively. Its time penod 5. A particle performs simple harmonic motion with
is amplitude A. Its speed is trebled at the instant that
it is at a distance 2 A/3 from equilibrium position.
v2 +v2 The new amplitude of the motion is
xf-,2 (b) 21t 1 2
(a) 21t 2 xf +xJ
vr-v2 (a) A f (b) 3A
vr-v[ (d) 21t v2
xf +xi
+ v2 (c) A✓3 (d) ~
(c) 21t xf-xJ 1 2 3
(AIPMT 2015) . (JEE Main 2016)
. . a solid oscilla tes in si?1ple 6. Two pendulums of time period 3 s and 8 s
3. A silver atom _in ·n some direct ion with a respectively start oscillating simultaneously from
harmo nic mot101n2 1 d What is the force
freque ncy O f 1o /secon •
ting one atom Wt•th
two opposite extreme positions. After how much
f the bonds connec time they will be in the same phase ?
constant O
the other ?
2, {ll) 3, (b) 5. (,I)
1, (b)
 24 12 1O. A mass m is performing linear sim
(a) - s (b) ple hannoni
s
5 5 mo tion , the n wh ich of the foll ow ing
grap~
24 represents correctly the variation of acce
(c) - s 12 a cor res pon ~ng to linear velocity
leratio
(d) - s v ? n
11 11
7. The radius of circle, the period of FIGURE 14(CF).2
revolution,
init ial pos itio n and sen se of rev olu v2
tion are v2
inclicated in the Fig. l 4(CF). l. y-projectio
n of the
radius vector of rotating particle Pis :

FIGURE 14(CF).1
y ..___ _ _ _ _,.a2

P (t = 0)
0 G
v2
v2

-------a2
(a) Y(t) = - 3 cos 2 7t t, where y is in
m . e e
(b) Y(t) = 3co s 31t t , where y 1s
. .
1n m 11. A particle executing SH M from an
2 extreme end
of the path towards the centre is observed
to be at
( c) y (t) = 3 cos -7tt , where y 1s
. .
1n m distances x 1, Xi and x from the centre, at
3 the ends
2 of three successive seconds. Its time
period of
(d) Y(t) = 4 sin 1tt , where y is in m
2
8. A particle of mass m is executing osc
(NEET 2019)

illation about
oscillation is [ use, cos 8 = ; \ : ~ 1
the origin on the x-axis, its potential (a) 2 1t/0 (b) 2 1t0
energy is
U = k x3, where k is a positive constan
amplitude of oscillation is a, the n its tim
Tis
(a) proportional to 1/ ✓ a
t. If the
e period (c) 8/2 7t 2
(d) ( ;
12. The acceleration versus displacemen
J
t graph of a
( b) independent of a par ticl e per for min g SH M is sho wn
in Fig.
14(CF).3. The time period of oscillation of
(c) proportional to ✓ particle
a (d) proportional to a 3'2. in second is
9. The density p of a liquid varies with
depth h from FIGURE 14(CF).3
the free surface as p = k h. A small body
of density a(m s-2 )
p 1 is released from the surface of liquid. The
body
will
(a) com e to a momentary rest at a dep
th 2 p 1/k
from the free surface
(b) execute S.H.M. about a point at a dep
th p 1/k
from the sur face
(c) execute S.H.M. of amplitude p /k
1
(d) all of these

6. (b) 7. (c) 8. (a) 9. (d) 10. (d) 11. (a)

 (a) 21tx.fi (b) i1tx ✓3 . (a) an ellipse (b) a straight line
(c) a parabola (d) a circle .
(c) 2 'It X (2) 114
I
(d) 2 7t X (3) 114
19. A particle moves' with . simple
• harmoru~ • mouon
13. If the displacement x and velocity v of a particle
in a straight line. In first t s, after s ~ g from
executing SHM are related through the expression rest it travels a distance a, and in next t 5 it travels
2
4 v = 25 - :x?- t then its time period is
distance 2 a in same directiont then
(a)61t (b)41t
(a) amplitude of motion is 4 a
(c) 3 Jt (d) 2 1t
(b) time period of oscillation is 6 t
14. The velocity vector v and displacement vector x (c) amplitude or'motion is 3 a
of ~ particle executing SHM are related as (d) time period of oscillation is 8 t
. [JEE (Main) 2014]
-vdv = -ro2x w1'th the 1rut1
•• ·a1 cond'ttion
• v = v at
0
dx 20. Two particles ~e oscillating a]ong two close
x = 0. The velocity v, when displacement is x, is parallel straight lines side by side with the same
frequency and amplitude. They pass each othe_r,
(a) v = Jv5 + o.>2x2 (b) v . .Jv5-ro2x 2 • moving in opposite directions when their
displacement is half of the amplitude. ~e m~an
(c) v = Vv~ + oi3x3 positions of the two particles lie on a stra1gh_t line
perpendicular to the paths of the two particles.
(d) v = v 0 -(ro3x3eX3 )113 (AIIMS 2015)
The phase diffe~nce is
15. If x, v and a denote the displacement, the velocity (a) 0 (b) 2 tr/3
and the acceleration of a particle executing SHM (c) 7t (d) tr/6
of time period T. Then which of the following . (AIPMT (Main) 2011)
does not change with time ? • 21. The displacement y of a particle executing
(a) aT/x (b) aT + 2 7t v periodic motion js given by
(c) aT/v (d) a2 T2 + 4 1t2 v 2 y = 4 cos2 (tfl) sin (1000 t)
(AIEEE 2009) This expression inay be considered to be a result
of the superposi~on of
16. Two particles A and B describes SHM of same
(a) two (b) three
amplitude a and frequency v along the same
straight line. The maximum distance between two (c) four • J •

(d) five independent harmonic motions.

particles is Jj a . The initial phase difference 22. Four simple hatjnonic motions ; x 1 = 8 sin Ci)I ;
between the particles is : ,ti . 6 sin (rot-+: 7r/2) ; .r3 = 4 sin (9 + 1t) and
(a) 2 tr/3
x4 = 2 sin (CM + ~ tr/2) are superimposed on each
(b) tr/6
other. The resulting amplitude and its phase
(c) 'lfl3 (d) 1Cl2 difference with f I are respectively
17. A particle is 'performing simple harmonic mo~on
(a) 20, tan-I (1/2) (b) 4Ji., 7C/2
along x-axis with amplitude 4·0 cm and time I

period 1·2 s. The minimum time taken by the (c) 20, tan-I (2) i (d) 4..fi.,7C/4
particle to move from x = ~ 2 cm to x = + 4 cm
I
23. Two particles P fDd Q are executing SHM across
and back again is same straight li;ne whose equations are given
(a) 0·3 s (b) 0•4 s as Yp = A sin(~+ ♦1) and Yo= A COS (mt+ +i).
An observer, at ( = 0 observes the particle P at a
(c) O·S s (d) 0· 2 5
18. A particl~ is subjected to two . mutually distance A 1./i. moving to the right fro~ mean
1
perpendicular SHMs such that x = 2 s10 fJ>/ and • ! . .Jj
• position O wbil~ particle Q at - A moving to

J= 2sin(GY+i J I
the left from tnqan position O as shown in Fig.
14(CF).4. Then ~ - ♦ 1 (in rad) is equal to
2

. The path ofthe particle will be i

16. (a) 17. (b} 11. (a) 19. (b). ~ 20. (b) 21. (b~ 22. (d)
12. (d) • 13. (b) 14. (b) 15. (11) .
 FIGURE 14(CF).4
(1) y = sin (J)I ~, cos CJlt (2) y
+- 3
(3) y = 5cos( :-3wt)
a 0
(4) y = 1 + cot + co2 t2
(a) 5 n/6 (b) 3 7t/4
(a) Only (1)
{c) 5 1r./2 (d) 7 7t/12
(b) Only (4) docs not represent SHM
24. A particle of mass 5 kg is placed in a field of
(c) Only (1) and (3)
gravitational potential
(d) O~y (1) and ~2) (AIPMT 20U)
.
V = (7 x2 - 21 x) J/kg. Then its motion
(a) is SHM with angular frequency l •67 rad/s 29. A particle execuung simple harmonic motio f
(b) is SHM with angular frequency 3.74 rad/s amplitude A, along x-axis, about x = 0. Wbc: 1~
potential energy equals kinetic energy, the positi
(c) is oscillatory but not SHM on
of the particle will be :
{d) is SHM with amplitude 5·5 m
25. A particle of mass 2 kg moving along x-axis has (a) A (b) A
potential energy given by, U = 16x2- 32 x (in joule), 2 M
where x is in metre. Its speed when passing A
through x = 1 m is 2 ms-1 ;
(c) -:Ji (d) A (JEE Main 2019)

(a) the motion of particle is a uniformly accele- 30. A particle is executing simple harmonic motion
rated motion with a time period T. At time t = 0, it is at its
(b) the motion of particle is an oscillatory from position of equilibrium. The kinetic energy-time
x = 1·S m to 3·0 m graph of the particle will look like
(c) the motion of particle is not a simple harmonic I FIGURE 14(CF).5
motion
(d) the period of oscillatory motion is 7t/2 s
26. The function sin• (co t) represents
(a) a simple harmonic motion with a period 1C/co (a)
t-+
(b) a simple harmoni c motion with a period
21C/co
(c) a periodic, but not simple harmonic motion
with a period woo
(d) a periodic but not simple harmonic motion
with a period 2 1C/co (b)
T t-+
0 T/4 T/2
27. A point mass is subjected to two simultaneous
sinusoidal displacements in x-direction,
2
x 1 (t) = A sin mt and %z (t) = A sin (mt+ 3!C)

Adding a third sinusoid al displace ment (c)

X] (t) • B sin (a+ , ) brings the mass to a complete 0 T/2 T
rest. The value of B and , are
r=
(a) "'..c,A, 431t (b) A, 34Jt
'
Jt
/Z
(c) 'ti., A, 651t (~ A,3 (DT 2011)
(d)
28. Out of the followin g function s represen ting
motion of a particle, which represents SHM ?
(JEE l\1aln 2011>
----- ----- ----- -.~zt R/IJ :IDJ J___ ___ ___ ___...... ~

23, (d) M, (b) 21. (d) 26, Cc) 27, (b) 21, (c) 29, (c) • . 30, (b) ·
31. A body is executing SHM. At a displ
· tial • accmcnt x (a)4n (b)n
~ts potcn 'al energy ~s E1 and at a displacement y'
its potcntl energy 1s E 2. The potential . ' (c) 2 n (NEET 2021)
(d) 3 n
a displacement (x + y) is ,___ energy at 36. A spring is stretch by 5 cm by a force 10 N • ~e
15
time period of oscillations when a mass of 2 kg
(a) E1 + E2 (b) .JEi E2 suspended by it is :
(~) J£i2 +Ei (d) El+ E2 +2.JE1 E2 (a) 0· 628 s (b) 0-0628 s
(c) 6·28 s (d) 3•14 s (NEET 2021)
32. For a simple pendulum, a graph is plotted bet·
. ki . (KE ween 37. A simple harmonic motion is represented by :
its . ne~c c?ergy ) and potential energy (PE)
against its displacement d. Which of the following = 5 [sin 3 1U + ../3 cos 3 1tl] cm
y
represents these correctly ? (Graphs arc schematic
and not drawn to scale) The amplitude and time period of the motion are :
2 2
FIGURE 14(CF).8
(a) 10 cm,
3
s (b) 5 cm,
3s
I(s) E (b) E
(c) 10 cm, -s
3
s(d) S cm,
3
I K.E. P.E.
2 2
(JEE Main 2019)
38. This displacement-tim e graph of a particle
,/ K.E. executing SHM is given in Fig. 14(CF).7 (sketch
d d is schematic and not to scale).
(cf) FIGURE 14(CF).7
tE P.E.

K.E.

'\ \
d
\
I
4T
I 4

(JEE Main 2015)

33. Average velocity of a particle executing SHM in Which of the following statements is/are true for
one complete vibration is : [Take amplitude of this motion ?
oscillation A and uniform angular velocity ro]. (A) The force is zero at t = 3 T/4
(B) The acceleration is maximum at t = T
A co
(a)- (b) Ao> (C) The speed is maximum at t = T/4
2
(D) The PE is equal to KE of the oscillation at t
= T/2
(c) Ac; (d) zero (NEET 2019)
(a) (B), (C) and (D) (b) {A). (B) and (D)

34. Identify the function which represents a periodic (c) (A) and (D) {d) (A). (B) and (C)
motion. (JEE Main 2020)
(a) e--OY (b) e(J)/
39. 1\vo simple harmonic motions are given by
(d) sin Cl)I + cos (J)I
(c) logt (rot)
(NEET 2020) Xi = ~ [sin (2 7tt) + ros (2 7tt)],
. . h onic motion with
35. A body is executing s1mp1e ann . tiaJ
-½ = 5 [sin (2 1tt + 7t/4)]
frequency 'n •. The frequency of its poten
energy is:
ANSWERS
/) 34 (ti) 3$. (c) 36. (,,) 37. (u) 38. (J)
31. (,() 32. (/,) J_'\. (, •
 The ratio of amplitude of the given motions is
'
(a) .Ji: l (b) 2 : 1 a _l_ K-Adg
1/2
b _.!_ [ K+Adg]-!2
( ) 21t [ M ] ( ) 21t M
(~) I: ..fi. (d) I : 2

~
' 112
(JEE Main 2021) c _1_ [ K + Ad g ] _l_ [ K - Ad g ]-
40. A body is executing S.H.M. The velocity (V) vis ( ) 21t M (d) 21t M
wsition (x) graph of a body in SHM is 45. An ideal gas enclosed in a cylindrical container
(a) straight line (b) parabola suppons a freely moving piston of mass M. The
(c) circle (d) ellipse piston and the cylinder have equal cross-sectional
(JEE Main 2021) area A. When the piston is in equilibrium, the
41. The displacement of simple harmonic oscillator volume of the gas is V0 and its pressure is p
after 3 seconds starting from its mean position is The piston is slightly displaced from th:
• equal to half of its amplitude. The time period of equilibrium position and released. Assuming that
hannonic motion is : the system is completely isolated from its
(a) 6s (b) 8 s surrounding, the piston executes a simple
harmonic motion with frequency
(c) 12 s (ti) 36 s
(JEE Main 2022) _1_ yAP0 _1_ VoMPo
(a) (b)
21t V0 M 27t yA2
42. ~e equation of a particle executing simple
hannonic motion is given by
1) . . (c) _l_ ✓yA 2 P0 (d) I ✓ yA
MY0
: x =sin A (3 =
t+ i m. At 1 s, 21t MV0 21t
(JEE Main 2013)
2P
0

tlie speed of the particle will be :

46. A simple pendulum is oscillating without
((liven it= 3-14) damping, Fig. 14(CF).8. When the displacement
(a) 0 cms-1 · (b) 157 cms-1 of the bob is less than maximum, its acceleration
I
(c) 272 cms-1 (ti) 314 cms-1 --+
I vector a is correct! y shown in
(JEE Main 2022)
FIGURE 1,(CF).8
'IL Simple pendulwn, Spring osdllations
'
1 and other harmonic oscillations
43. A pendulum bob bas a speed of 3 ms-1 at its
lowest position. The pendulum is 0-5 m long. The 0 G
speed of the bob, when the length makes an angle
of fH to the vertical, will be (if g = 1O ms-2)
(a) (1/3) ms-l (b) (1/2) ms-1
I
(c) 2 ma-1 (ti) 3 ms-1 -+
a
44. ~ uniform cylinder of length Land mass M having
c~••-aectional area A is suspended with its
v ~ length from a fixed point by a massless
s,rina, auch that it is half submerged in a liquid G
of density 'tf, at equilibrium position. When the
er.Under is aiven a small downward push and
~ it starts oscillating vertically with a small
8'll)litude. If the force constant of the sprina is ➔
a
JG the frequency of oscillation of the cylinder is
' •

'.• 39. (c) •• (d) 41. (d) 42. (b) 43. (c) 44. (c) 45. (c) 46. (c)
 at one en d to t he cc1.1mg.
.
The period of
mge period becomes T2, when the e)ev~tor;mo~eds
• a, its ume peno
. . . sma11 down with an accelerauon
osc1llat1on 1s 1
becomes 73, then !
(a) T = 21t~ (b) T =1t$ T. +T. ,:;:-;;- I
(a) 7i = 2 3 (b) 7i = -V~ 2 7j I
2 I

(c) T =21t/li . (d) T =21t/f T.2 r:3 (d) T,

.J2 T2 T3
= --;::::::==;=:=
(c) 7i = J /.r.2 + 7:2
'V/T2
2
+ 7..2
3
"/' 2 3
48. Two simple pendulums have time period T and
5 T/4. They start vibrating at the same instant from 52. A simple pendulum oscillating in air has; period
T. The bob of the pendulum is compl~tely
the mean ~sition in the same phase. The phase
difference (1n rad) between them when the smaller immersed in a non-viscous liquid. The density of
I
I
pendulum completes one oscillation will be
the liquid is - 1 th of the material of the I bob. If
7t 7t 16 !
(a) - (b) - the bob is inside the liquid all the time, its period
6 5
of oscillation in this liquid is : ,
~
1t
(c) - (d) f
2 s fT (T
49. A simple pendulum has time period 7 1. The point
(a) 2T
vw (b) 2T
V14
)

i•
of suspension is now moved upward according
to relation, y = kt2. (k = 1 ms-2), where y is the (c) 4T /I (d) 4T /1
vertical displacement. The time period now vis V14
(JEE Main 2019)
becomes T2 . The ratio of T.21Tl is (g = 10 ms-2) 53. A spring of force constant k is cut into lengths of
ratio I : 2 : 3. They are coMected in series and
(a) 615 (b) S/6
the new force constant is k'. Then they are
(c) 1 (d) 4/5 connected in parallel and force constant is k".
SO. A simple pendulum of length Lis suspended from Then le' : k" is
the top of a flat beam of thickness IJ2. The bob is (a) 1 : 6 (b) 1 : 9
pulled away from the beam so that it m~es :111 (c) I : 11 (d) 1 : 14 (NEET 2017)
angle 8 < 300 with the vertical, as shown 1~ Fig. 54. Three springs are connected to a mass m as shown
14(CF).9. It is then released from rest. If ♦ 1s the in Fig. 14(CF).10. When mass oscillates, the
maximum angular deflection to the right, then effective spring constant and time period of
vibrations respectively are : [Given k = 2 Nim
FIGURE 14(CF).I and m = 80 gram]
FIGURE 14(CF).10
U2 ..... ,:.;.,,,,.,

--
m

(a) ♦ = 8 (b) ♦ ~ 2 8
(c) ♦ < 8 (d) 8 < ♦ < 2 8
ded fl m the roof of an
51. A pendulum suspen . ~ T , when the
elevator at rest has ~ UlDe leratic!a O its time

I ,.:el:e:v•:t:o:r:mo:v:e:s:u:p~wi~th~an•acce~~- ~~~!~~~~~,Y-Y.;,,

a.
1 ) ,,::a:.. (d) 52. (c)
(a) - '"' " · ,a
S3. (c)
 (a) 8 Nm- , 0-628 s (b) 6 Nm- , 0-628 s 58. Four massless springs whose force constants are
1
(c) 8 Nm- , 0-526 s (d) 6 Nm-1, 0-526 s 2 k, 2 k, k and 2 k respectively arc attached to
55. A body of mass m falls from a height h on the pan mass M kept on a frictionless plane (as shown ~
of a spring balance. The masses of the pan and Fig. 14(CF).12. If the mass Mis displaced in th
spring are negligible. The spring constant of the horizon tal directio n a little and left, then th:
spring is k. The body gets attached to the pan and frequency of the system is ,
starts executing SHM in the vertical direction. The
.
I

FIGURE 14(CF).12
amplitude of the oscillation is
k
2k 2k
(a) mg ✓• + 2/ch FIGURE 14(CF).11
M
k mg
0 h
t;.:;. tveC d ,.. 1 •• ~ ◄• ,a,

(b) fI(1 + 2kh)

~;;, mg
(a) 217t ✓ 4~ 1 ffik
(b)- -

(c) ff (1+ ~~) k

1 fT
21t

1
M

/7k
(c) 21t ~7M (cf) 21tVM 0
'

(ti)~
mg
✓1+ 2/ch m 59. A particle of mass m is fixed to one end of a light
mg spring of force constant k and unstretched length
56. A block of mass m, attached to a spring of spring l, Fig. 14(CF).13. The system is rotated about the
constant le, oscillates on a smooth horizontal table. other end of the spring with an angular velocity
The other end of a spring is fixed to a wall. The ro, in gravity-free space. The increase in length of
block has a speed v when the spring is at its natural the spring will be
length. Before coming to an instantaneous rest, if FIGURE 14(CF).13
Ct)
the block moves a distanc e x from the mean
position, then k
---m
(a) x=~.!!!.. (b) x=-
1 -*
kv k
V
(a) mco t
2 m«r I
(c) x=v t Cd) x=~T
r,;;v k
(b) k+mro2

mco2 l (d) none of the above

57. One end of a long metallic wire of length Lis tied (c) k 2
-mco
to the ceiling. The other end is tied to massless
60. Two blocks A and B of FIGURE 14(CF).14
spring of sprin& constant k. A mass m hangs freely masses 2 m and m,
from the free end of the spring. The area of cross- respectively are connected
section and Young's modulus of the wire are A by a massles s and
and Y respectively. If the mass is slightly pulled inextensible string. The
down and released, it will oscillate with a time whole system is sus-
period T equal to pended by a m~ssl~ss
spring as shown 1n F•~· A
(a) 2K.Jm/ k 14(CF) .14. The magni-
tude of the acceleration of
(b) 2,,c.Jm(YA + k L)I YAk A and B, imfDediately after t

(c) 2xJmY A/ k L (d) 2tc.JmL IYA.

. the string is cut, are
respectively
B
I
m
•
--·
54. (a) 55. (a) 56. (c) 57. (b) 58. (b) 59. (c)
 (a) g, g/2 (b) g/2, g
63. A block of mass m, lying on a smoo~ ~orizon':1
(c) g, g (d) g/2, g/2 surface, is attached to a spring (of negligible ~ )
61 . A mass of 2·0 kg is put on a flat pan attached to a of sprink constant k. The other end of the spnng
vertical spring fixed on the ground as shown in is fixecL as shown in the Fig. 14(CF). l 7• The block
Fig. t4(CF).15. The mass of the spring and the is initially at rest in equilibrium position. now I!'
pan is negligible. When pressed slightly and the block is pulled with a force F, the maximum
released the mass executes a simple harmonic speed of the block is :
motion. The spring constant is 200 Nm-1. What FIGURE 1'(CF).17
should be the minimum amplitude of motion so

~. .«::
that the mass gets detached ~rom the pan.
(Take g = 10 ms-2)
FIGURE 14(CF).15
m
(a) J; (b) 1C.Jmk
F

---- F

--- (c) ; ; (d) Jmk

(JEE Main 2019)
64. A uniform rod of length L and mass Mis pivoted
at the centre. Its two ends are attached to two
(a) 10·0 cm (b) 8-0 cm springs of equal spring constant Jc. The springs
are fixed to rigid suppons as shown in Fig.
(c) 6·0 cm
14(CF).18, and the rod is free to oscillate in the
(a) any value less than 10·0 cm (AIPMT 2007)
horizontal plane. The rod is gently pushed through
62. A block of weight W produces an extension of a small angle 8 in one direction and released. The
9 cm when it is hung by an elastic spring of length frequency of oscillation is
60 cm and is in equilibrium. The spring is cut
into two parts, one of length 40 cm and the other FIGURE 14(CF).11
of length 20 cm. The same load W hangs in
equilibrium supported by both parts as shown in
Fig. 14(CF).16(b). The extension in cm now is
FIGURE 14(CF).11

6 l f8
( a )1- -
2K M &" (b)- -I&
2K M
~
.
6
0

·i _!_~k __!_J24t
l
(c) • (d)
M

w
l 2K 2K M
(DT 2009)
65. Th~ mass ~ s~own in the Pia. 14(CF).19.
0 osc11late1 10 11mple harmonic motion with
(a) 2 (b) 3 amplitude A. The amplitude of point p is
(c) 6 (t/)9
I
,'
l I 11 I 1115-111111 •• I IHI <wee
.... (6) ,1. (Cl) Q.(o) 63.(d) 6'. (c) mull
 FIGURE 14(CFt.19 (a) of l?~ same frequency and with shifted ¾a
I
posttion.
•
rncan
k1 k2 1 (b) of the same frequency and with th • •
M positi~n. e same mean
p
(c) of c_h~nged frequency and with shifted •
pos1tton. mean
(d) of changed frequency and with the sarn
.. e mean
pos1tton. . (IJT 2
68 A • • • 011)
• • mass M, attached. to a horizontal· spnng •
k1 A i k2 A . executes S.H.M. with amplitude A 1• Wb' •
(c) k + k • (d) k +k (UT 2009) . en the
1 2 l I 2. mass M passes through
. its mean positi~n thcna
m er mass m 1s p1aced over it and both of th
Sall
66. A particle of mass m is attached to three identical
move together with amplitude A2. The ratioc:
springs of spring consta~t k as shown in Fig.
l 4(CF).20. The time peri of vertical oscillation
' of the particle is (~ }s '
~IGURE 14(Cf').20
.I . . (a) M +m (b) ( i'2
.M
M M+m)

(c) (M;mr (d) M

) M+m
I

l (AIEEE 2011)
69. If a spring of stiffness 'k' is cut into two parts 'A'
and •B' of length IA : IB =2 ·: 3, then the stiffness
of spring 'A• is given by
5 (b) 3k
(a) -k
I '2 .
.,
~
5
(a) 27t* (b} 21t ~
I lli (c) 2k (d) k (AIEEE2011)
)
5
~
,' m 70. A particle with restoring force proportional to
(c) 2Jt (d)IJt~
-
~3k :I k displacement and resisting force proportional to
(WB JEE 2010) velocity is subjected to ·a force F sin o>t. If the
I amplitude of the particle is maximum for ro = 001
67. A wooden block performs SHM on a frictionless and the energy of the particle maximum for
surface with frequency, Vo- The block carries a· m ~ then (<.t>o is the angular frequency of
=
charge + Q on its surface. If now a uniform electric
• undamped oscillations)
➔
field E is switched o_n as shown in Fig. (a) m1 = Wo and <0i ~ 00o
14(CF).21, then the SHM of the block will be • (b) (1) 1 = <a>o and CJ>-i = CJ>o
FIGURE 14(CF).21 (c) (1)1 ~ (llo and Cl)i =CJ>o
➔ (d) (1)1 ~ 0>o and <62 ~ Wo·
E ► 71. The amplitude of a damped oscillator decreases
to 0·9 times its original magnitude in 5. 5: ~
+Q
another 10 s it will decrease to x times ongin
magnitude, where x equals :
ANSWERS
65. (d) 66. (b) 67. (a) 68. (c) 69. (a) 70. (c)
.
 (a) 0·1, (b) 0·81
75. What will be the time period of oscillation, if the
(c) 0-729 (d) 0-6.
length of a second pendulum is one third ?
. , (JEE Main 2013)
72. If a simple penduJum has significant am rt (a)(213)s (b) (1/./J)s
1 d
, (upto a factor of lie of original) only in th p ~ e
_ e~n~ (c) (2/ ✓3)s (d) 4/ ✓Js
between~ - 0 s tot= 'ts, then 't may be called the
average hfe of the pendulum When th 76. What is the frequency of a seconds pendulum in
• esphencal
.
an elevator moving up with an acceleration of
bob. of the pendulum .suffers a retardat·ion (d ue to
viscous drag) proportional to its velocity, with 'b' g/2?
as. the constant
f of proportionality
. , the average 1Ue
1:" (a) l ·225 s-1 (b) 0-612 s-1
tune o the pendulum 1s (assuming da • . (c) 0-408 s- 1 (d) 1·837 s-1
small) in seconds : mpmg is
77. If the length of a correct pendulum clock is raised
0-693 by O· 1%, what will be the effect on the time of
(a) b (b) b
the clock in a day ?
I (a) Time loss per day is 43·2 s
(c) - (d) 2
b (AIEEE 2012) (b) Time loss per day is 86·4 s
b
73. ~ rod. of mass M an~ length 2 L is suspended at (c) Time gain per day is 43·2 s
its middle by a wue. It exhibits torsional (d) Time gain per day is 86·4 s
oscillations. If two masses each of m are attached 78. In damped oscillations, the amplitude of
at distance U2 from its centre on both sides it oscillations is reduced to one fourth of its initial
reduces the oscillation frequency by 20%. The value 10 cm at the end of 50 oscillations. What
value of ratio mlM is close to : will be its amplitude when the oscillator
(a) 0·11 (b) 0·51 completes 150 vibrations ?
(c) 0-37 (d) 0-17 (a) 0·078 cm (b) 0· 156 cm

(JEE Main 2019) (c) 0·312 cm (d) 0-122 cm

74. A thin strip 10 cm long is on au shaped wire of 79. A simple pendulum of length 1 m is oscillating
negligible resistance and it is connected to a spring with an angular frequency 10 rad/s. The support
of spring constant 0·5 Nm- 1 Fig. 14(CF).22. The of the pendulum starts oscillating up and down
assembly is kept in a uniform magnetic field of with a small angular frequency of I rad/s and an
0· 1 T. If the strip is pulled from its equilibrium amplitude of 10-2 m. The relative change in the
position and released, the number of oscillations angular frequency of the pendulum is best given
by
it petforms before its amplitude decreases by a
factor of e is N. If the mass of the strip is 50 gram, (a) 10-3 rad/s (b) 10-1 rad/s
its resistance 10 n and air drag negligible, N will (c) 10-s rad/s (d) I rad/s
be close to: .. (JEE Main 2019)
80. ~e mass and the diameter of a planet arc three
FIGURE 14(CF).22 ttm~s the re~pective values for the Eanh. The
penod. of oscillation.of a simple pendulum on the
X X X Earth is 2 s. The penod of oscillation of the same
X
10cm
pendulum on the planet would be
X B X X 2
X X X (a) - s 3
(b) -s
Jj 2
(a) 50000 (b) 10000 ~s
(c) - (d) 2.Jis
(c) 1000 2
(d) 5000
(JEE Main 2019) (JEE Main 2019)

72. (d) 73. (c) 74. (d) 75. (c) 76. (b) 77. (a) 78.(b) 79. (a) 80. (d)