If $x, v$ and $a$ denotes 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^{2} T^{2} + 4 π^{2} v^{2}

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a T / x

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a T + 2 π v

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a T / v

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Solution

The correct option is B $a T / x$
We know that,
$a = - ω^{2} x$ ( $∵$ particle executes SHM)
Muliplying on both sides with $\frac{T}{x}$ we get
$\frac{a T}{x} = - ω^{2} T$
$(∵ ω = \frac{2 π}{T})$
$\Rightarrow \frac{a T}{x} = - \frac{4 π^{2}}{T} =$ constant
Hence option (b) is correct.

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