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>> $A simple harmonic motion has an amplitud$

Question

A simple harmonic motion has an amplitude $A$ and time period $T$ . The time required by it to travel $x = A$ to $x = \frac{A}{2}$ is:

A

$T / 6$

B

$T / 4$

C

$T / 3$

D

$T / 2$

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Updated on : 2022-09-05

Solution

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Correct option is A)

$x = A cos ω t$
$t = 0, x = A$
At $x = \frac{A}{2}$ ,
$\frac{A}{2} = A cos ω t$
$ω t = \frac{π}{3}$
$\frac{2 π}{T} t = \frac{π}{3}$
$t = \frac{T}{6}$ where T is time period

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