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?

a^{2} T^{2} + 4 π^{2} v^{2}

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\frac{a T}{x}

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a T + 2 π v

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\frac{a T}{v}

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Solution

The correct option is B $\frac{a T}{x}$
$\frac{a T}{x} = \frac{ω^{2} x T}{x} = \frac{4 π^{2}}{T^{2}} T = \frac{4 π^{2}}{T} = c o n s t a n t$

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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?

The correct option is B aTxaTx=ω2xTx=4π2T2T=4π2T=constant

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?

The correct option is B $\frac{a T}{x}$
$\frac{a T}{x} = \frac{ω^{2} x T}{x} = \frac{4 π^{2}}{T^{2}} T = \frac{4 π^{2}}{T} = c o n s t a n t$