Have been stuck with this question from classical mechanics under the simple harmonic motion the question is saying that if $$y=a\cos(\omega t)+b\sin(\omega t)$$ show it represents simple harmonic motion also find its amplitude, period and frequency. how can I show that it represents the simple harmonic motion?


closed as off-topic by Gert, ZeroTheHero, John Rennie, Qmechanic Aug 20 at 16:27

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  • $\begingroup$ Think about either $c\cos{(\omega t+\delta)}$ or $c\sin{(\omega t+\delta)}$. $\endgroup$ – G. Smith Aug 20 at 15:45

A system described by a function $x(t)$ exhibiting simple harmonic motion obeys the following differential equation $$\frac{\text d^2x}{\text dt^2}=-Cx$$ where $C$ is some constant. The idea here is that there is a force that is trying to restore the system to equilibrium ($x=0$), and this force is proportional to how far away the system is from this equilibrium.

If you can verify that your solution obeys this differential equation, then you have shown it describes simple harmonic motion. I will leave that to you to figure out.

  • $\begingroup$ Yes, but this doesn’t explain how to get the amplitude, period, and frequency. $\endgroup$ – G. Smith Aug 20 at 18:13
  • $\begingroup$ @G.Smith The problem asks for those things, but OP just asked how to show it represents SHM. I assumed the OP already knew how to handle the other parameters, which is why they only asked about SHM. $\endgroup$ – Aaron Stevens Aug 20 at 18:28

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