I was trying to understand why a spring -mass assembly and a simple pendulum is a simple harmonic movement.(adsbygoogle = window.adsbygoogle || []).push({});

I've done like this:

In a SHM that starts in -A, we have x = -A.cos(wt)

In a spring-mass we have that the maximum velocity is [itex] \frac{mv²} {2} = \frac{kA²}{2} -> v = A\sqrt{\frac{k}{ m}} [/itex]

[itex] w = v/A = \sqrt{\frac{k}{m}} [/itex]

[itex] v = \int a.dt = \int \frac{-k.x}{m} dt [/itex]

But in a SHM, [itex] v = -w .x.tan(wt) -> -w .x.tan(wt) = \int \frac{-k.x}{m} dt [/itex]

If we substitute x = -A.cos(wt), we see that the expression is true, so spring-maass is a SHM.

But I don't know how to demonstrate why pendulum is a SHM?

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# Homework Help: Why a spring-mass assembly is a SHM?

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