First slide

Simple hormonic motion

Question

A particle is executing simple harmonic motion along a straight line with amplitude 2 cm. When the particle is at a distance of 1 cm from its equilibrium position, its velocity is equal to $4 c m s^{- 1}$ . Then time period of oscillation is

Easy

A

$π / \sqrt{2}$
B

$\frac{π}{2} \sec$
C

$\frac{π}{\sqrt{3}} s$
D

$\sqrt{3} \frac{π}{2} s$

Solution

$V = ω \sqrt{A^{2} - x^{2}} \Rightarrow V = ω A \sqrt{1 - \frac{x^{2}}{A^{2}}} \Rightarrow V = V_{m} \sqrt{1 - \frac{x^{2}}{A^{2}}}$
when $x = \frac{A}{2}, V = 4 \frac{C m}{s}$
$∴ T = \frac{2 π}{ω} = \frac{2 π}{4 / \sqrt{3}} \sec = \frac{\sqrt{3} . π}{2} \sec$

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