question_answer

The oscillation of a body on a smooth horizontal surface is represented by the equation, \[X=A\cos (\omega t)\] where X = displacement at time t \[\omega =\]frequence of oscillation Which one of the following graphs shows correctly the variation a with f? Note:- Here a = acceleration at time t T= time period

A)  

B)

C)

D)

Correct Answer: C

Solution :

 Displacement, \[x=A\cos (\omega t)\](given) Velocity, \[v=\frac{dx}{dt}=-A\omega \sin (\omega t)\] Acceleration, \[a=\frac{dv}{dt}=-A{{\omega }^{2}}\cos (\omega t)\] Hence graph  correctly depicts the variation of a with t.