Question

what is the frequency of the total energy of a particle in SHM​

Answer 1

Answer:

the total energy simple harmonic motion is the sum of its potential energy kinetic energy ,thus the total energy is simple harmonic motion of a particle.

Answer 2

The frequency of the total energy of the particle is zero.

Explanation:

The total energy of a particle in SHM​  is

$T.E=P.E+K.E$

We know that

The general equation of position of simple harmonic motion

$x=a\sin(\omega t)$

Where, a = amplitude

x = position

The velocity of the particle is

$v=a\omega\cos(\omega t)$

Now, the acceleration of the particle is

$a=-a\omega^2\sin(\omega t)$

The kinetic energy of the particle  is

$K.E = \dfrac{1}{2}mv^2$

Put the value of v into the formula

$K.E=\dfrac{1}{2}m(a\omega\cos(\omega t))^2$

$K.E=\dfrac{1}{2}ma^2\omega^2\cos^2(\omega t)$

The potential energy of the particle is

$P.E=\dfrac{1}{2}kx^2$

Put the value of x into the formula

$P.E=\dfrac{1}{2}k(a\sin(\omega t))^2$

Where, $k=\omega^2 m$

$P.E=\dfrac{1}{2}m\omega^2a^2\sin^2(\omega t)$

Now, The total energy is

$T.E=K.E+P.E$

$T.E=\dfrac{1}{2}ma^2\omega^2\cos^2(\omega t)+\dfrac{1}{2}m\omega^2a^2\sin^2(\omega t)$

$T.E=\dfrac{1}{2}ma^2\omega^2(\sun^2(\omega t)+\cos^2(\omega t))$

$T.E=\dfrac{1}{2}ma^2\omega^2$

Time period is infinity.

So, The frequency is

$frequency=\dfrac{1}{T}$

$frequency=\dfrac{1}{\infty}$

$frequency = 0$

Hence, The frequency of the total energy of the particle is zero.

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Topic : total energy of the particle

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