Question

A particle performing linear S.H.M. has a period of 6.28 seconds and a pathlength of 20 cm. What is the velocity when its displacement is 6 cm from mean position ?

Answer 1

Here, $T=6.28sec$,

Path length $=20cm\Rightarrow a=10cm=10\times {10}^{-2}m$

$x=6\times {10}^{-2}m$

$\omega =\frac{2\pi }{T}=\frac{2\pi }{6.28s}=1rad/s$

$v=\pm \omega \sqrt{(a^2-x^2)}$

$v=\pm \omega \sqrt{(100-36)\times {10}^{-4}}$

$1\times 8\times {10}^{-2}$

$\therefore v=8\times {10}^{-2}m/s$