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Question
Identify which of the following system exhibit simple harmonic motion?
I. A simple pendulum with small deflection.
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
Identify which of the following system exhibit simple harmonic motion?
I. A simple pendulum with small deflection.
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
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Solution
The correct option is D I and II only
Necessary condition for SHM is: F∝−x where, F=restoring force and x= displacement from mean position , negative sign shows that restoring force should be opposite to displacement.When a ball is coming down from a height, there is no restoring force and, when it goes up restoring force (mg) and displacement are in opposite direction but force is not directly proportional to displacement, it is constant for the whole displacement so it violates the necessary condition of SHM, whereas other two systems fulfill the condition.
Necessary condition for SHM is: F∝−x
where, F=restoring force and x= displacement from mean position , negative sign shows that restoring force should be opposite to displacement.
When a ball is coming down from a height, there is no restoring force and, when it goes up restoring force (mg) and displacement are in opposite direction but force is not directly proportional to displacement, it is constant for the whole displacement so it violates the necessary condition of SHM, whereas other two systems fulfill the condition.
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