First slide

Stress and strain

Question

If the displacement (x) and velocity (v) of a particle executing simple harmonic motion are related through the expression $4 v^{2} = 25 - x^{2}$ , then its time period is

Moderate

A

$π$
B

$2 π$
C

$4 π$
D

$6 π$

Solution

$4 v^{2} = 25 - x^{2},$
Differentiating both sides with respect to t
$4 (2 v \frac{dv}{dt}) = - 2 x \frac{dx}{dt} \Rightarrow 4 \frac{dv}{dt} = - x \Rightarrow 4 a = - x \Rightarrow a = - \frac{1}{4} x \Rightarrow ω^{2} = \frac{1}{4} \Rightarrow T = \frac{2 π}{ω} = 4 π other method comparing v = ω \sqrt{A^{2} - x^{2}} here v = \frac{1}{2} \sqrt{25 - x^{2}} ω = \frac{1}{2}$

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