Question

When the amplitude of illation of a particle in S.H.M. is increased to two times, the time period
(A) Is doubled
(B) Is halved
(C) Is unaltered
(D) Increased to $ \sqrt 2 $ times

Answer 1

Hint :The simple Harmonic Motion is an Oscillatory motion under which the retarding force is proportional to the amount of the displacement from an equilibrium position. The Amplitude is the maximum displacement of an object from the equilibrium position. Here we will find the correlation between amplitude and the time period.

Complete Step By Step Answer:
Any simple Harmonic Motion can be expressed by –
 $ x = A\sin (\omega t) $
Where A is the amplitude and $ \omega $ is the angular frequency.
Angular frequency can be defined as the $ \omega = \dfrac{{2\pi }}{T} $
Where “T” is the time period.
Given that if the amplitude is doubled then the time period also becomes doubled.
Hence, from the given multiple choices – the option A is the correct answer.

Additional Information:
Amplitude is the maximum displacement which is related to the energy in the oscillation. When it is displaced from the equilibrium, the object performs the simple Harmonic motion and its maximum speed can be achieved when it passes through equilibrium. Use velocity to time relation equation for amplitude. Time period is the time taken by the body to complete one oscillation. It can be defined as the $ T = \dfrac{{2\pi }}{\omega } $ where $ \omega $ (omega) is the angular frequency and T is the time period.

Note :
Always remember the correct formula for the simple harmonic function. When there is maximum displacement of the angle, the sine function is always equal to one. Always frame the correct equation based on the given data, check it twice.