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I thought that if we take a body which is performing Simple Harmonic Motion and take its reflection on a wall. Now we observe the reflection on the wall and so we can say the reflection is performing SHM without a force acting on it.

Is it right? Or there is something wrong in it

Please also give suitable Examples if possible.

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    $\begingroup$ Do you consider a reflection to be a "body"? $\endgroup$
    – The Photon
    Jan 8, 2022 at 16:08
  • $\begingroup$ I meant i am observing it $\endgroup$
    – Ayush Shankaram
    Jan 8, 2022 at 16:19

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The motion of SHM is given by $x(t)=A\cos(\omega t+\phi)$. Therefore, the acceleration is $\ddot x(t)=-\omega^2A\cos(\omega t+\phi)$, and the net force by Newton's second law is $F=\ddot x(t)=-m\omega^2A\cos(\omega t+\phi)$. So no, you cannot have SHM without a net force

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  • $\begingroup$ Thank You Very Much @BioPhysicist $\endgroup$
    – Ayush Shankaram
    Jan 8, 2022 at 18:46
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It is even easier than that: just voluntarily take a pen and paper, and draw a sine curve. No force involved!

But, joking apart, force is called the thing that depends linearly on displacement and drives a mass onto a simple harmonic motion in time. If you are willing to deviate from that definition, anything becomes possible, including fairies and elves.

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  • $\begingroup$ Thank You Very Much @Oliver for the Answer Understood it $\endgroup$
    – Ayush Shankaram
    Jan 8, 2022 at 18:43

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