First slide

Simple hormonic motion

Question

If the displacement $(x)$ and velocity (v) of a particle executing simple harmonic motion are related through the expression $9 v^{2} = 36 - x^{2}$ , here x is in meter and V is in m/s. Then time period of vibration is

Easy

A

$4.5 π \sec$
B

$\frac{8 π}{3} \sec$
C

$4 π \sec$
D

$6 π \sec$

Solution

$\begin{array}{l} 9 V^{2} = 36 - x^{2} \\ \Rightarrow V = \frac{1}{3} \sqrt{{(6)}^{2} - {(x)}^{2}} \end{array}$
Comparing this equation with the standard equation $V = ω \sqrt{A^{2} - x^{2}}$ , we can write $ω = \frac{1}{3} r a d / s$
$∴ T = 2 π / ω = \frac{2 π}{1 / 3} \sec = 6 π \sec$

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