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If x, v and a denote the displacement, v...

If `x, v` and a denote the displacement, velocity and acceleration of a particle exceuting simple harmonic motion of time period `T`, then, which of the following does not change with time.
(1) `a^(2)T^(2) +4pi^(2)v^(2)` (2) `(aT)/(x)`
(3) `aT = 2piv` (4) `(aT)/(v)`

A

`a^(2)T+4pi^(2)v^(2)`

B

`aT/x`

C

`aT+2piv`

D

`aT/v`

Text Solution

Verified by Experts

The correct Answer is:
B
For a simple harmonic motion, acceleration,`a=-omega^(2)x` where `omega` is a constant `omega=(2pi)/T` .
Hence , `a=-4pi^(2)/T^(2) ximplies (aT)/(x)=-(4pi^(2))/T`.
The period of oscillation T is a constant `thereforr(aT)/x` is a constant
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