UNIVERSITY OF EDUCATION,

JAUHARABAD CAMPUS

LAB MANUAL

BS Computer Science

(1st Semester)

Academic Year: 2024-2028

What is Science? Lab

GSCI1111

Prepared By

Mam Amina Batool

 Practical # 01

Find the value of "g" using simple Pendulum.

Objective:

To measure the acceleration due to gravity using a simple pendulum.

Using a simple pendulum, plot it's L-T2 graph.

Introduction:

The simple pendulum shown in Figure 1 is a mass "m" suspended from a point (O,
assumed to be frictionless), using a rod of neglected mass and length L. When the
pendulum is displaced from its equilibrium position and then released, it oscillates
about that equilibrium position, swinging back and forth along a semi-circular trajectory.
During its oscillation, the pendulum is subject to restoring force due to gravity g.

Theory:

The simple pendulum executes Simple Harmonic Motion (SHM) as the acceleration of
the pendulum bob is directly proportional to its displacement from the mean position
and is always directed towards it.

The time period (T) of a simple pendulum for oscillations of small amplitude, is given by
the relation,

T = 2π.√L/g

Gravitational acceleration,

g = 4π.L/T2

Diagram:
Apparatus and Materials

1. Iron stand

2. Digital Stopwatch

3. Meter ruler

4. Thread

5. Pendulum bob with hook

6. Cork

7. Vernier calliper

Procedure:

1. Find the vernier constant and zero error of the vernier callipers.

2. Measure the radius (r) of the bob using a vernier callipers.

3. Measure the length of hook (h) and note it on the table.

4. Since h and r is already known, adjust the length of the thread l to make L = l + h
 + r an integer (say L = 60cm) and mark it as M1 with ink. Making L an integer will
make the drawing easier. (You can measure the distance between the point of
suspension (ink mark) and the point of contact between the hook and the bob
directly. Hence you get l + h directly).

5. Similarly mark M2, M3, M4, and M5 on the thread as distance (L) of 70 cm, 80 cm,
90cm and 100cm respectively.

6. Pass the thread through the two half-pieces of a split cork coming out just from
the ink mark (M1).

7. Tight the split cork between the clamp such that the line of separation of the two
pieces of the split cork is at right angles to the line along which the pendulum
oscillates.

8. Fix the clamp in the stand and place it on the table such that the bob is hanging
at-least 2 cm above the base of the stand.

9. Mark a point A on the table (use a chalk) just below the position of bob at rest
and draw a straight line BC of 10 cm having a point A at its centre. Over this line
bob will oscillate.

10. Find the least count and the zero error of the stop clock/watch. Bring its hands at
zero position

11. Move the bob by hand to over position B on the right of A and leave. See that the
bob returns over line BC. Make sure that bob is not spinning.

12. Now counting oscillations, from the instant bob passes through its mean
position A, where its velocity is maximum.

13. Now start the stop watch at the instant the bob passes through the mean
position A. Go on counting the number of oscillations it completes. As soon as it
completes 10 oscillations, stop the watch. Note the time t for 10 oscillations in
the table.

14. Repeat the measurement at least 3 times for the same length.

15. Now increase the length of the thread by 10 cm (M2) and measure the time t for
this length as explained from step 6 to 14.

16. Repeat step 15 for at least 3 more different lengths.

Observation and calculation:

Observe diameter of the bob:

(i) ______cm, (ii)________cm, (iii)___________cm

Mean diameter of bob, d/3= d' = _________cm

The radius of the pendulum of the bob = ______________cm

Length of the hook = ______ cm

Mean = L/T2 = _______________________

Result:

We know, T = 2 π √ (L/g)

Experimental value,

g = 4π2(L/T2) = ______________________
Graph:

L vs T graph

Plot the graph between L and T from the observations recorded in the table. Take L
along X-axis and T along Y-axis. The L-T curve is a parabola. The origin need not be (0,0)
point.

L vs T2 Graph
2 2
T = (4π /g)×L or

T2 = KL (K= constant)

Plot the graph between L and T2 from the observations recorded in the table. Take L
along X-axis and T2 along Y-axis. The L-T curve is a straight line passing through the (0,
0) point. So the origin of the graph should be chosen (0, 0).
Precautions :

1. The thread should be very light and strong.

2. The point of suspension should be reasonably rigid.

3. The pendulum should oscillate in the vertical plane without any spin motion.

4. The floor of the laboratory should not have vibration, which may cause a
deviation from the regular oscillation of the pendulum.

5. The amplitude of vibration should be small (less than 15) .

6. The length of the pendulum should be as large as possible in the given situation.’

7. Determination of time for 20 or more oscillations should be carefully taken and

repeated for at least three times.

8. There must not be strong wind blowing during the experiment.

Viva Questions
Q.1: What is simple Pendulum?

Ans: A small metal ball (called bob) or a mass suspended from a fixed point by a
long thread such that the bob is free to swing back and forth under the influence
of gravity.

Q.2: Why the word ‘SIMPLE’ is used before the pendulum?

Ans. Because the pendulums used in the wall clocks are ‘COMPOUND
PENDULUMS’, in which a metallic rod is used in place of the thread.

Q.3: What is the relation between frequency and time period?

Ans. f = (1 / T) or T = (1/F)

Q.4: What are the units of frequency?

Ans. Vibrations / sec, cycles / sec (c.p.s.) or Hertz.

Q.5: What is the frequency of a second pendulum?

Ans. 0.5 Hz or (1 / 2) Hz, because

f = ( 1 / T ) = (1 / 2)

( T = 2 s for a second’s pendulum).

Q.6: Prove that g = 4 π2 (L / T2).

Ans. For a simple pendulum time period is given by:

T = 2 π √L/g

T2 = 4 π2 L/g

i.e. g = 4 π2 L/T2

Where L = length of the simple pendulum.

Q.7: What is restoring force?

Ans. The force which tends to bring a vibrating body towards the mean position.
Q.8: Can you replace the thread by a rubber band?

Ans. No, because it is not inextensible. By definition the string must be

inextensible.

Q.9: Why the pendulum stops after some time?

Ans. Its energy is lost as heat.

Q.10: What is a seconds Pendulum?

Ans. a seconds pendulam is a pendulam which takes two seconds for one
oscillation.

Q.11: What is the length of the simple pendulum?

Ans. The distance between point of suspension of the pendulam and its center of
gravity(bob) is called as length of simple pendulam.

Q.12: What is the shape of the L-T graph of simple pendulum?

Ans. Shape of L-T graph is a parabola.

Q.13: What is the shape of the L-T2 graph of a simple pemdulum ?

Ans. Shape of L-T2 graph is straight line.

Q.14: Does a simple pendulum stop finally? Why?

Ans. Yes, because of the air resistance on the pendulum and the frictional force
between the string and the pivoted point.

Q.15: What is time period of simple pendulum?

Ans. Time taken by bob of the simple pendulam to make one complete vibration,
is called as the time period of simple pendulam.

Q.16: What is the relation between the period of simple pendulum and
acceleration due to gravity?

Ans. The period of a simple pendulam is inversely propotional to the square root
of acceleration due to gravity.

Q.17: The relationship between the period of a simple pendulum and the length
of pendulum?
Ans. The period of a simple pendulam is directly propotional to the square root of
length of pendulam.

Q.18: What is an oscillation?

Ans. One complete to and fro movement of a pendulam about it's mean position
is known as an oscillation or vibration.

Q.19: What is the frequency of simple pendulum?

Ans.The no.of oscillations made by the pendulam in one second is called it's
frequency (Hz).

Q.20: Is the period of a simple pendulum is dependent of the amplitude of

oscillation?

Ans. No, the period of a simple pendulam is independent of the amplitude of

oscillation.