# Simple harmonic motion qsn [closed]

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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• Think about either $c\cos{(\omega t+\delta)}$ or $c\sin{(\omega t+\delta)}$. – 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.