Hi guys, I was just wondering what the answers are for this question, as it says it's B, and I'm only getting C as an answer (attempted multiple times). Could anyone please just clarify what the answer is, and if it is B, any explanation would be great, but I'm not convinced that it is the answer.
I found the amplitude and used the condition $x=0, v=4$ to find my answer
Thank you
The period of the function $f(x)=\sin(ax)$ is given by $$2\pi /|a|.$$ From this we can rule out answer $A$ since $a$ must be equal to $2$. Now, if the velocity has a maximum value of $4$ then the amplitude of the derivative of the function $x(t)$ must be equal to $4$. The only function that satisfies this answer $C$. To prove, let $x(t)=2\cos(2t)$, therefore $$x'(t)=\frac{d}{dt}x(t)=2\cdot\frac{d}{dt}\cos(2t)=-4\sin(2t).$$