Question

A body is in simple harmonic motion with time period half second $(T=0.5s)$ and amplitude one cm $(A=1cm)$. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.

• A. $4cm/s$
• B. $6cm/s$
• C. $12cm/s$
• D. $16cm/s$

Answer 1

Answer: (C)

$12cm/s$

Average velocity is simply the displacement of the particle divided by time taken.
Simple harmonic motion can be described by $x=A\sin \omega t$ where $\omega =\frac{2\pi }{T}$ if the particle starts at the mean position at t=0
time when particle reaches$x=\frac{A}{2}$ is when $\omega t={\sin }^{-1}\frac{1}{2}$ which is $t=\frac{1}{24}$ seconds
Total displacement is $A/2$
Hence average velocity = $\frac{1/2cm}{\frac{1}{24}s}$ = $12cm/s$