2023TrialMultiple choice

Q8

1 mark

Question

A particle is travelling in simple harmonic motion such that its velocity, in metres per second, is given by the equation

v^2=a^2-b^2x^2,

where $a,b\ne0$ . What is the period of motion?

(A) $\displaystyle \frac{2b\pi}{a}$

(B) $\displaystyle \frac{2a\pi}{b}$

(D) $\displaystyle \frac{2\pi}{b}$

Try the question before revealing the answer.

Solution

Answer: D

v^2=b^2\left[\frac{a^2}{b^2}-x^2\right]

n=b

T=\frac{2\pi}{b}

\int 2v\,dv=\int dx

\frac{2v^2}{2}=x+C\quad\therefore\quad v^2=x

\frac{dv}{dx}=\frac{1}{2v},\qquad v\frac{dv}{dx}=\frac12,

a=\frac12.

$(D)$

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Mechanics

Simple harmonic motionDerive and interpret displacement, velocity and acceleration models for simple harmonic motion.

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