Question

An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object's maximum speed V_max?

a) T and V_max both double.
b) T remains the same and V_max doubles.
c) T and V_max both remain the same.
d) T doubles and V_max remains the same.
e) T remains the same and V_max increases by a factor of squareroot 2.

Answer 1

b) T remains the same and V_max doubles.

Step-by-step explanation:

As we know that the time period of oscillation is given as

`T = 2\pi\sqrt{(m)/(k)}`

so it is independent of the amplitude of oscillation

So if we increase the amplitude then it will not change the time period of the oscillation

Now the maximum speed of the oscillation is given as

`v = A\omega`

now if we increase the amplitude then maximum speed will also increase

so correct answer will be

b) T remains the same and V_max doubles.