Question

A body executing linear simple harmonic motion has a velocity of $3cm/s$, when its displacement is $4cm$ and a velocity of $4cm/s$, when its displacement is $3cm$. What is the amplitude of oscillation?

• A. $5cm$
• B. $7.5cm$
• C. $10cm$
• D. $12.5cm$

Answer 1

The correct option is A $5cm$

In SHM, the velocity $V$ at a displacement $x$ is given by
$V=\omega {(A^2-x^2)}^{\frac{1}{2}}or{V}^2={\omega }^2(A^2-x^2)$
Now
$V=3cm/s$
When,
$x=4cm.\therefore 9={\omega }^2(A^2-16)......\left(i\right)$

Also
$V=4cm/s$
When,
$x=3cm\therefore 16={\omega }^2(A^2-9)......\left(ii\right)$
Simultaneous solution of equations $\left(i\right)$ and $\left(ii\right)$ gives
$A=5cm$