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?

  • Option 1)

    a^{2}T^{2}+4\pi ^{2}v^{2}\;

  • Option 2)

    \; \; \; aT/x\; \;

  • Option 3)

    \; aT+2\pi v\;

  • Option 4)

    \; \; aT/v

 

Answers (1)

As we learnt in

Simple Harmonic Motion -

It is special case of oscillatory motion of a vibrating particle in which the acceleration at any position is directly propotional to displacement from mean position & it is directed towards mean position.

- wherein

\vec{a}\; \alpha -\vec{x}

 

 x=A\ sin(\omega t+\phi)

a=-A\omega^{2}sin(\omega t+ \phi)

So \frac{aT}{x}=-\omega^{2}x

Correct option is 2.

 


Option 1)

a^{2}T^{2}+4\pi ^{2}v^{2}\;

This is an incorrect option.

Option 2)

\; \; \; aT/x\; \;

This is the correct option.

Option 3)

\; aT+2\pi v\;

This is an incorrect option.

Option 4)

\; \; aT/v

This is an incorrect option.

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