Question
The maximum acceleration is a and the maximum velocity is v. What is the amplitude?
$\frac{\text{a}_{\text{max}}}{\text{v}_{\text{max}}}=\frac{\text{a}}{\text{v}}=-\omega,$
Also $\text{v}=\omega\text{A}=\frac{\text{a}}{\text{v}}\text{A}$
$\therefore\text{A}=\frac{\text{v}^2}{\text{a}}$
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$\text{I}\propto\frac{1}{\text{r}}$
$\text{I}\propto\frac{1}{\text{r}^2}$
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$\text{I}\propto\frac{1}{\text{r}^4}$