# Q. 14.24 (c) A body describes simple harmonic motion with an amplitude of $5\; cm$ and a period of $0.2\; s.$ Find the acceleration and velocity of the body when the displacement is (c)  $0 \; cm$

A = 5 cm = 0.05 m

T = 0.2 s

$\\\omega =\frac{2\pi }{T}\\ \omega =\frac{2\pi }{0.2}\\ \omega =10\pi\ rad\ s^{-1}$

At displacement x acceleration is $a=-\omega ^{2}x$

At displacement x velocity is $v=\omega \sqrt{A^{2}-x^{2}}$

(a)At displacement 0 cm

$\\v=10\pi \sqrt{(0.05)^{2}-(0)^{2}}\\ v=10\pi \times 0.05\\v=1.57ms^{-1}$

$\\a=-(10\pi )^{2}\times0\\a=0$

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