Question

A body executing $S.H.M.$ along a straight line has a velocity of $3m{s}^{-1}$ when it is at a distance of $4m$ from its mean position and $4m{s}^{-1}$ when it is at a distance of $3m$ from its mean position. Its angular frequency and amplitude are:

• A. $2rad{s}^{-1}$ & $5m$
• B. $1rad{s}^{-1}$ & $10m$
• C. $2rad{s}^{-1}$ & $10m$
• D. $1rad{s}^{-1}$ & $5m$

Answer 1

The correct option is D $1rad{s}^{-1}$ & $5m$

Velocity $v=\omega \sqrt{A^2-X^2}$

$3=\omega \sqrt{A^2-4^2}$...(1)

$4=\omega \sqrt{A^2-3^2}$...(2)

$\frac{3}{4}=\frac{\sqrt{A^2-4^2}}{\sqrt{A^2-3^2}}$

$\frac{9}{16}=\frac{A^2-16}{A^2-9}$

$16A^2-9A^2={16}^2-9^2$

$7A^2=175$

$A^2=25$

$A=5$

From (1), $3=\omega \sqrt{5^2-4^2}$

$\omega =1rad/sec$