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Can we draw a relation between Time period and amplitude an object doing SHM? I came up with something but I’m not sure if it’s correct.

$TA = k$, where k is a constant

I came up with this just by observing the graph of SHM. When the time period of SHM is high it’s amplitude is low and vice versa. I’m not sure if I need to modify this any way shape or form. Besides, if this is correct, then what is the formal mathematical proof for this?

Any help will be appreciated.

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An SHM is governed by the equation of motion:

$$y=A\sin\left(\omega t+\varphi\right)$$

where $A$ is the amplitude, $\omega=\frac{2\pi}{T}=\sqrt{\frac{k}{m}}$ and $\varphi$ a phase angle (constant for a given SHM)

Clearly $T$ and $A$ are independent of each other: any $A$ can be imposed for any $T$. $T$ only depends on the ratio $\frac{k}{m}$.

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