Question

The time period of a particle undergoing Simple Harmonic motion is $16s$ . It starts motion from the mean position. After $2s$ , its velocity is $0.4 \, ms^{- 1}$ . The amplitude is

• A. $1.44m$
• B. $0.72m$
• C. $2.88 \, m$
• D. $0.36 \, m$

Answer 1

Answer: (A)

Velocity, $v=r\omega cos \omega t;$
$0.4=r\times \frac{2 \pi }{16}cos \frac{2 \pi }{16}\times 2=r\times \frac{2 \pi }{16}\times \frac{1}{\sqrt{2}}$
or $r=\frac{0.4 \times 16 \times \sqrt{2}}{2 \pi }=\frac{3.2 \sqrt{2}}{\pi }=1.44 \, m$