Question

What is the frequency of the kinetic energy of a body in shm if the time period of shm is t?

Answer 1

Dear Student,

◆ Answer -

Frequency of the kinetic energy of a body in SHM = 2/t

● Explanation -

Given that the time period of SHM is t. As we know, frequency of SHM is reciprocal of time period, so frequency of SHM is 1/t.

But frequency of kinetic energy of body is twice its frequency of SHM. Hence, the frequency of the kinetic energy of a body in SHM is 2/t.

Thanks dear. Hope this helps you...

Answer 2

The frequency of the kinetic energy of a body in shm is $\frac{\omega}{\pi}$.

Explanation:

• In case of simple harmonic motion the velocity is given by the change in direction divided by change in time. v(t) = $\frac{dx}{dt}$ and  $\frac{dx}{dt}$ = - Aω sin (ωt + φ)
• To know the time period for V(t)  here is actually the time period sin(ωt) Which when seen in function is $\frac{2\pi}{\omega}$.

Now $\frac{1}{2} mv^2$, is the formula for kinetic energy.

As we know it so in case of time period (t) kinetic energy will be

                                              k(t) = $\frac{1}{2} mv(t)^2$

                                  ⇒ k(t) = $\frac{1}{2} m\omega^2 A^2 sin^2$ (ωt + φ) .

• Here, the kinetic energy for time period will be the value for $sin^2$ (ωt) which is equal to $\frac{\pi}{\omega}$ and since frequency is the Reciprocal of time period.

So, time period for kinetic energy when inverted will give the frequency as $\frac{\omega}{\pi}$.

To know more:

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