A particle describes linear SHM Its velocities are 3ms

| A particle describes linear S.H.M. Its velocities are

3 m s^{- 1}

and

2 m s^{- 1}

when its displacements are 2 m and 3 m respectively from mean position. Find length of the path?

A. 1.2 m

B. 4.6 m

C. 6.7 m

D. 7.2 m

Please scroll down to see the correct answer and solution guide.

Right Answer is: D

SOLUTION

$v = ω \sqrt{A^{2} - x^{2}}; \frac{3}{2} = \frac{\sqrt{A^{2} - 4}}{\sqrt{A^{2} - 9}}$
Squaring, $\frac{9}{4} = \frac{(A^{2} - 4)}{(A^{2} - 9)}$
$9 A^{2} - 81 = 4 A^{2} - 16; 5 A^{2} = 65$
$A^{2} = \frac{65}{5} = 13; A = \sqrt{13} m$
$∴$ Length of the path $= 2 A = 2 \sqrt{13} = 7.2 m .$

A particle describes linear SHM Its velocities are 3ms

Right Answer is: D

SOLUTION

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