Simple Harmonic Motion (SHM) is a unique type of periodic motion where the restoring force is directly proportional to the displacement, but acts in the opposite direction. The formula for Simple Harmonic Motion helps us calculate the position, velocity, acceleration, and time period of an object undergoing SHM.
Key Formulas for Simple Harmonic Motion
Note: The terms in the above formulas represent:
A = amplitude (m)
Sample Problems involving SHM
Example 1:
A pendulum swings with an amplitude of 0.10 m and an angular frequency of 3.14 radians/second. What will be the position of the pendulum after 3 seconds, given that the phase shift is 0 radians?
Solution:
Given,
A= 0.10 m
t= 3 seconds
Using the position formula,
Substituting the given values, we get
Solving this, we find the position of the pendulum at t=3 seconds.
X = 0.10 m.
Example 2:
An object in SHM has an amplitude of 4 cm and a period of 0.1 s. Determine the acceleration and velocity of the object when the displacement is (a) 4 cm (b) 2 cm (c) 0 cm.
Solution:
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