The amplitude of simple harmonic oscillation is doubled.  How would this affect :

(i)  Time period

(ii)  Maximum velocity

(iii)  Acceleration at mean position,

(iv)  Kinetic energy at mean position?

 

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

(i)  The time period of oscillation of simple harmonic oscillator is

Since the time period is independent of amplitude of vibration, therefore, time period remains unchanged on doubling the amplitude of oscillation.

(ii)  Maximum velocity of particle undergoing simple harmonic oscillation is

Where A is amplitude.  On doubling the amplitude the maximum velocity becomes twice.

(iii) Acceleration at mean position is zero, independent of amplitude of vibration.  Therefore, acceleration at mean position remains unaffected.

(iv)  Kinetic energy at mean position

If amplitude of oscillation gets doubled, then kinetic energy at mean position increases to four times.

Answered by  | 4th Jun, 2014, 03:23: PM