Question

The oscillation of body on a smooth horizontal surface is represented by the equation,
$x=A\cos \left(\omega t\right)$
Where
$x=$ displacement at time $t$
$\omega =$ frequency of oscillation
Which one of the following graphs shows correctly the variation ${}^{\prime }{a}^{\prime }$ with ${}^{\prime }{t}^{\prime }$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Displacement, $x=A\cos \left(\omega t\right)$
Velocity, $v=\frac{dx}{dt}=-A\omega \sin \left(\omega t\right)$
Acceleration, $a=\frac{dv}{dt}=-A{\omega }^2\cos \left(\omega t\right)$
Hence $C$ is the correct option.