Question

The position x of a body is given by x = A sin wt. Find the time at which the displacement is maximum​

Answer 1

PLZ refer to the attachment

for answer

Remember

maximum displacement will be when

Sinwt = 1

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Answer 2

Given that,

The position x of a body is given by :

$x=A\sin \omega t$

To find,

Time at which the displacement is maximum​.

Solution,

For maximum displacement put $\dfrac{dx}{dt}=0$

$\dfrac{dx}{dt}=\dfrac{d(A\sin \omega t)}{dt}\\\\\dfrac{dx}{dt}=A\cos \omega t{\cdot} \omega\\\\A\cos \omega t{\cdot} \omega=0\\\\\cos \omega t=0\\\\\omega t=(2n+1)\dfrac{\pi}{2}$

if n = 0

$\omega t=(2n+1)\dfrac{\pi}{2}\\\\\omega t=\dfrac{\pi}{2}\\\\t=\dfrac{\pi}{2\omega}$

Hence, this is the required solution.

Learn more,

Trigonometry

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