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The oscillation of body on a smooth horizontal surface is represented by the equation,$X=A \cos (\omega t)$Where$\mathrm{X}=$ displacement at time $\mathrm{t}$$\omega=$ frequency of oscillationWhich one of the following graphs shows correctly the variation ‘a’ with ‘t’?
The oscillation of body on a smooth horizontal surface is represented by the equation,
$X=A \cos (\omega t)$
Where
$\mathrm{X}=$ displacement at time $\mathrm{t}$
$\omega=$ frequency of oscillation
Which one of the following graphs shows correctly the variation ‘a’ with ‘t’?
Physics
The oscillation of body on a smooth horizontal surface is represented by the equation,
$X=A \cos (\omega t)$
Where
$\mathrm{X}=$ displacement at time $\mathrm{t}$
$\omega=$ frequency of oscillation
Which one of the following graphs shows correctly the variation ‘a’ with ‘t’?

Option A:

Option B:

Option C:

Option D:

Solution:

The correct option is C

Displacement is given as $x=A \cos (\omega t)$
Velocity is given as $\mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=-\mathrm{A} \omega \sin (\omega \mathrm{t})$
Acceleration is given $a=\frac{d v}{d t}=-A \omega^{2} \cos (\omega t)$

Hence $C$ is the correct option.

i

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