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# 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 (b) 3 cm

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

(b)  $\inline 3\; cm$

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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 3 cm

$\\v=10\pi \sqrt{(0.05)^{2}-(0.03)^{2}}\\ v=10\pi \sqrt{0.0016}\\v=10\pi \times 0.04\\v=1.257ms^{-1}$

$\\a=-(10\pi )^{2}\times 0.03\\a=-29.61ms^{-2}$

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