Periodic Motion
If a motion on definite path repeats itself after a fixed time interval,
then this motion is known as periodic motion
Time period
The minimum time interval after which motion repeats itself is known as
time period
Frequency- No. of oscillations per second
Amplitude- maximum displacement from Mean Position
Vibration- Oscillation with very high Amplitude and high frequency.
T may or may not be constant,
force is Restoring and aways towards mean Position
Oscillation
A type of periodic Motion in which particle moves back and forth about a mean position
Earth's motion is not a oscillation but motion Pendulum is
It is not necessary that the end points in the oscillatory motion is fixed
If in Oscillatory Motion = Total Mechanical energy conserved then the end points will
be same
Linear simple Harmonic Motion
Oscillation with constant Amplitude and frequency.
Conditions for SHM
Extreme Position Mean position Extreme Position
Differential equation of SHM
Deriving equation of speed for SHM
Speed of Particle at Any time
Deriving Position of Particle in SHM
# velocity and accn of particle
-ve shows that acceleration is opposite to displacement
Draw graph between speed V and position X
(Max Velocity at Mean Position)
Removing the graph in the negative Y axis
because speed can’t be negative
Draw graph between acceleration a and position X
Kinetic Energy In SHM
Potential Energy In SHM
Total Energy In SHM
Total Mechanical conservation
Basic question
Equation Of SHM
Q. A particle on a planck is performing SHM in vertical direction.
Equation of SHM =
1. Find normal force on mass ‘m’
Extreme position
Mean position
Theory: since the particle is doing SHM, so it will have acceleration towards the mean position
This is the least value of normal performing SHM
Theory: since the particle is doing SHM, so it will have acceleration towards the mean position
At extreme position in SHM the acceleration is maximum
This is the largest value of normal performing SHM
SHM as projection of uniform circular motion
The radius of circle and the amplitude of SHM is same
Horizontal Planck
If a particle moves in a uniform circular motion, then its shadow will perform in oscillatory motion
Now proving this oscillatory motion as SHM
Since uniform circular motion or no tangential
Hence, it will perform SHM
Write down equation of SHM, whose amplitude is ‘A’ and angular frequency and
its initial position is as shown
Mean Position
Analysing second information about velocity to
Analysing this question through uniform circular motion method
So we have to analyse two situations because at T=0 there
are two positions on the circle, whose projection on the
horizontal plan is starting from mean position
If the particle projected velocity is going in the right direction means the particle had started
If the particle projected velocity is going in the left direction means a particle at started
from the bottom, where the value of phii becomes pie because the angle is 180°
Case 1
Case 2
Case 3
Case 4
Since velocity is going in the positive
Analysing this question through uniform circular motion method
Spring Mass System
Combination Of Spring
Angular SHM
Simple Pendulum
Physical or Compound Pendulum
Torsional Pendulum
Superposition Of SHM’s
Case - 1 Same direction Same omega
Case - 2 Same direction different omega
Case-3 Mutually Perpendicular Direction
Miscellaneous Questions
