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)

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, $a=\frac{dv}{dt}=\frac{d}{dt}(-A\omega \sin \omega t)$
$=-A{\omega }^2\cos \omega t$
Hence the variation of $a$ with $t$ is correctly shown by graph.