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JEE Main 2009 (AIEEE) · Velocity & Acceleration in SHM

Velocity & Acceleration in SHM question from JEE Main 2009 (AIEEE)

Q77JEE Main 2009 · AIEEEMedium

Velocity & Acceleration in SHM

If $x, v$ 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?

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Answer: (a)

In SHM $a = -\omega^2 x$ with $\omega = \dfrac{2\pi}{T}$ .
$\dfrac{aT}{x} = -\omega^2 T = -\dfrac{4\pi^2}{T}$ , a constant.
$aT + 2\pi v$ and $aT/v$ change with time because $a$ and $v$ change differently.
So the answer is (a) $aT/x$ .

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