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Wave Equation

The time peri...

Question

The time period of a particle performing linear SHM is 12s. The time taken by it to make a displacement equal to half its amplitude is

A

1 s

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B

2 s

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C

3 s

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D

4 s

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Solution

The correct option is B 1 s

$T = 12 s e c$
$ω = \frac{2 π}{T} = \frac{π}{6} \frac{r a d}{s e c}$
$x = A$ $s i n$ $ω t$
$x = A$ $s i n (\frac{π}{6} t)$
We want x to be $\frac{A}{2}$
Thus at t $=$ 1 sec we get $x = \frac{A}{2}$

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