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