A simple harmonic motion has an amplitude A and time period T. Find the time required by it to travel directly from $x = 0$ to $x = A / 2$ .

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Solution

Let, $A =$ amplitude

$T =$ time period

Equation of motion in S.H.M,

$x = A c o s (ω t)$ . . . . .(1)

at $x = 0$ , $c o s ω t_{1} = 0$

$ω t_{1} = \frac{π}{2}$

$t_{1} = \frac{T}{4}$ .

At $x = \frac{A}{2}$

$\frac{A}{2} = A c o s ω t_{2}$

$w t_{2} = \frac{π}{3}$

$t_{2} = \frac{T}{6}$

The total time required by the particle travel directly from $x = 0$ to $x = \frac{A}{2}$

$t = t_{1} - t_{2}$

$t = \frac{T}{12}$

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