2022TrialShort answer

Q14 (a) (i)

1 mark

Question

A particle is moving so that $v^2=n^2(a^2-x^2)$ . Show that the particle is moving in simple harmonic motion.

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Solution

Q.14(a)(i)

v^2=n^2(a^2-x^2)

=n^2a^2-n^2x^2.

\frac{d}{dx}(v^2)=-2n^2x

\ddot x=\frac d{dx}\left(\frac12v^2\right)=-n^2x.

Particle is moving with SHM.

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Syllabus alignment

Mechanics

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

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