Delta

L3CALC

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$\Delta ϵϵ24Q_3$:

A particle moving in simple harmonic motion obeys the law:

$$\frac{d^{2}x}{d{t}^2}=-w^{2}x$$

$\boxed{1}$ Show that:

$$\frac{d^{2}x}{d{t}^2}=v\frac{dv}{dx},\text{ where }v=\frac{dx}{dt}$$

$\boxed{2}$ Hence, show that:

$$v=\pm w\sqrt{A^2-x^2}\text{ if }v=0\text{ when }x=A$$