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Q.

A particle is making simple harmonic oscillations motion along x-axis. If at distances 3 cm and 5 cm from the mean position, the velocities of the particle are 13 cm/s and 5 cm/s respectively, the time period of oscillation is

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a

5π/6 s

b

3π/2 s

c

2π/3 s

d

2π/5 s

answer is C.

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Detailed Solution

$\begin{array}{l} v = ω \sqrt{A^{2} - x^{2}} \\ \begin{array}{l} \Rightarrow A = \frac{v^{2}}{ω^{2}} + x^{2} \Rightarrow \frac{v_{1}^{2}}{ω^{2}} + x_{1}^{2} = \frac{v_{2}^{2}}{ω^{2}} + x_{2}^{2} \Rightarrow ω^{2} = \frac{v_{1}^{2} - v_{2}^{2}}{x_{2}^{2} - x_{1}^{2}} = \frac{13^{2} - 5^{2}}{5^{2} - 3^{2}} = \frac{144}{16} \Rightarrow ω = 3 rad / s \\ \Rightarrow T = \frac{2 π}{ω} = \frac{2 π}{3} s \end{array} \end{array}$

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