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I came across this question:

A particle performs simple harmonic with amplitude A. Its speed is trebled at the instant that it is a distance 2A/3 from equilibrium position. The new amplitude of the motion is:

The solution to this question is given in this link: https://www.sarthaks.com/195678/a-particle-performs-simple-harmonic-motion-with-amplitude-a

However, I do not understand why the change in velocity only affects the amplitude, and not the angular frequency. After searching this site for a suitable answer, I found this:

Why does angular frequency of a particle in SHM does not change when it's velocity is changed

But doesn’t the change in velocity imply there must have been some acceleration, which would have been caused by some additional forces? So why doesn’t the angular frequency change?

Any help would be appreciated.

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2 Answers 2

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The harmonic oscillator has a fixed frequency that is governed the system properties. When you increase the velocity that means you are increasing its kinetic energy. This just means that it will go farther now than earlier, before turning back.

You are right in saying that the change in velocity occurs due to additional forces acting. But this means that the extra force is external. The oscillator on its own can’t do so.

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  • $\begingroup$ So, if the forces are external, they cannot change the angular frequency of the particle? $\endgroup$
    – SG_27
    Commented Feb 3, 2020 at 8:12
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    $\begingroup$ Not a force that acts momentarily. However a continuous force can forcefully oscillate an oscillator at arbitrary frequency. Think of holding a spring and compressing it at your will of frequency. But the natural frequency is always a system property. $\endgroup$ Commented Feb 3, 2020 at 9:35
  • $\begingroup$ Okay, that makes sense. Thank you. $\endgroup$
    – SG_27
    Commented Feb 3, 2020 at 11:44
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    $\begingroup$ Whether the force is external or internal is irrelevant. In both cases the force will not change the period unless it alters the system properties such as the stiffness of a spring. An internat force can increase kinetic energy for example through an explosion. $\endgroup$ Commented Feb 4, 2020 at 2:19
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In shm, amplitude changes in all the motion. In extreme position velocity is minimum while at mean position velocity is maximum. For in depth understanding read this article amplitude of shm

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