First slide

Periodic Motion

Question

Force on a particle is given by: F = -kxⁿ. For what values of n will the motion be oscillatory?(k is a positive constant)

Difficult

A

3 only
B

4 only
C

Any odd integer
D

It cannot be oscillatory for any value of n

Solution

For motion to be oscillatory there has to be an equilibrium position towards which the force is acting throughout the motion. In the expression, F = -kxⁿ,
If n is even, force will always act in one direction.
If n is odd, force will change direction when x changes direction and will always act towards the origin.
Hence, motion will be oscillatory if n is odd.
Thus, from the given options 3 is correct.

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