Question

A particle executing SHM in a straight line AOB is found to have zero velocity when it is at points A and B whose distance from O are 'a' or 'b', respectively, and its velocity is v when it is half-way between them. Find the frequency of oscillation.​

Answer 1

$\huge\bf{\underline{Solution:-}}$

$\small\sf{At\:point\:A\:and\:B\:velocity}$

$\small\sf{B\:zero\:m}$

$\rightarrow$$\small\sf{distance\:between\:A\:and\:B=a+b}$

$\small\sf{Amplitude\:of\:SHM=}$$\small\frac{a+b}{2}$

$\therefore$$\small\sf{at\:point\:M}$

$\small\sf{velocity=V}$

$\small\sf{but\:in\:SHM\:velocity\:at}$

$\small\sf{at\:mean\:position=AW}$

$\therefore$$\small\sf{AW=V}$

($\small\frac{a+b}{2}$)$\small\sf{W=V}$

$\small\sf{W=}$$\small\frac{2V}{a+b}$

$\small\sf{T=}$$\small\frac{2\pi}{w}=$$\small\frac{2\pi}{2V}(a + b)$

$\small\sf{T=}$$\frac{\pi(a + b)}{V}$