Question

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

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

Answer 1

Answer: (D)

$v=\omega \sqrt{A^{2}-x^{2}} $
$v_{1}=3 \,m / s \,\,x_{1}=4\, m $
$v_{2}=4\, m / s\,\, x_{2}=3\, m $
$3=\omega \sqrt{A^{2}-4^{2}} $ ... (i)
$4=\omega \sqrt{A^{2}-3^{2}}$ ... (ii)
iolving (i) and (ii), we get
$A=5 \,m $ and $\omega=1 \,rad / s$