Could someone please guide me through the following question. I honestly have no clue where to start. Thank you so much!
A particle moving in Simple Harmonic Motion starts from rest at a distance 10 metres to the right of its centre of oscillation O. The period of the motion is 2 seconds.
i. Find the speed of the particle when it is 4 metres from its starting point.
i. Find the time taken by the particle to first reach the point 4 metres from its starting point, in seconds correct to 2 decimal places.
The displacement from the center at any time $t$ is given by $$x(t) = 10\sin(\omega t) $$ where $$\omega =\frac{2\pi}{T} =\frac{2\pi}{2} =\pi \ \text{rad/s}$$ Note when $x=6$, $$6=10\sin(\pi t) \implies t=\frac{1}{\pi} \sin^{-1}\frac 35$$
and the velocity at $x=6$ is$$\frac{dx}{dt}\bigg|_{t=\frac{1}{\pi} \sin^{-1}\frac 35} =10\pi\cos\left(\sin^{-1}\frac 35\right)=8\pi \ \text{m/s}$$