Question

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 $\omega$ = frequency of oscillation Which one of the following graphs shows correctly the variation a with $t$ ?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

Here, X = A cos $\omega$ t $\therefore$ Velocity, v = $\frac { dX}{ dt} = \frac{ d}{ dt} \, ( A \, \cos \omega t )$ = - $A \omega \sin \omega t$ Acceleration, a = $\frac{ dy}{ dt} = \frac{d}{ dt} \, (- A \omega \sin \, \omega t )$ = $- A \omega^2 \, \cos \, \omega t$ Hence the variation of a with t is correctly shown by graph