Question

A mass m is attached to an ideal massless spring. When this system is set in motion with amplitude a, it has a period t. What is the period if the amplitude of the motion is increased to 2a?.

Answer 1

Time period is T if increasing the amplitude to 2A

What is Time period?

The length of time during which an activity occurs or a condition remains.

The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

Formula of Time period, T:

$T = 2\pi \sqrt{\frac{M}{k} }$

Where,

k is the spring constant

mass of system = M

Amplitude = A

Time period = T  

Here,

The amplitude is doubled = 2A

Since from the formula we can say that, The Time period is not dependent on amplitude.

Increasing the amplitude implies increase in the restoring force. An increase in the restoring force means the mass is now accelerated to cover more distance in the same period.

So the restoring force cancels the effect of the increase in amplitude.

Hence,

Time period is T if increasing the amplitude to 2A

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