The oscillation of a body on a smooth horizontal surface is represented by the equation, where = displacement at time = frequency of oscillation Which one of the following graphs shows correctly the variation of with Here = acceleration at time ,

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Solution

Q.
The oscillation of a body on a smooth horizontal surface is represented by the equation, $X = A \cos (ω t)$

where $X$ = displacement at time $t$

   $ω$ = frequency of oscillation

Which one of the following graphs shows correctly the variation of $a$ with $t$

Here $a$ = acceleration at time $t$ , $T$ = time period   [2014]

1

2

3

4

Ans.
(3)

Here, $X = A \cos ω t$

$∴$ $Velocity, v = \frac{d X}{d t} = \frac{d}{d t} (A \cos ω t) = - A ω \sin ω t$

$Acceleration, a = \frac{d v}{d t} = \frac{d}{d t} (- A ω \sin ω t) = - A ω^{2} \cos ω t$

Hence the variation of $a$ with $t$ is correctly shown by graph (3).

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