Question

A spring pendulum oscillates in a vertical plane such that the time period of the oscillation is T. if the whole setup is hung from ceiling of an elevator moving up with an acceleration g/2, then the time period of oscillation of the spring will be ​

Answer 1

Answer:

Time period of spring block system does not depend upon g therefore if g changes ,time period will remain constant =T,

T=2πkm​

​=2πgl​

​

it seems that T depends upon g ,but as the g changes , l  will also change and the ratio gl​ will remain constant.

Explanation:

Answer 2

Given:

A spring pendulum oscillates in a vertical plane such that the time period of the oscillation is T. if the whole setup is hung from ceiling of an elevator moving up with an acceleration g/2.

To find:

New time period of oscillation ?

Calculation:

The general expression of time period of a spring is :

$\sf \: T = 2\pi \sqrt{ \dfrac{m}{k} }$

• 'm' is mass , 'k' is spring constant.

This expression doesn't depend on gravitational acceleration, hence independent of 'g'.

• So, whenever elevator moves with acceleration of g/2 upwards, the value of the time period does not change.

• This is applicable only for spring pendulum.

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• But if the question asked for a simple pendulum, the case would have been different.