JEE Main · 2009 · 12 Apr 2009 · Offline · Elasticity & SHM

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x, v

and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

(A) $a^{2} T^{2} + 4 π^{2} v^{2}$
(B) $\frac{a T}{x}$ ✓ Correct
(C) $a T + 2 π v$
(D) $\frac{a T}{v}$

Answer: (B)

Solution

In simple harmonic motion the acceleration is tied to the displacement by

a = - ω^{2} x

, where

ω = \frac{2 π}{T}

. Forming the combination

\frac{a T}{x}

removes the displacement entirely, leaving

- ω^{2} T = - \frac{4 π ^{2}}{T}

, which depends only on the fixed period and so stays constant throughout the motion. The other combinations still contain quantities that change as the particle oscillates.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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