Can u average (sine)ing function?

Calculus Level 4

A body is executing 1D motion along the \(y\)-axis. It's displacement as a function of time is given by \(y=A\sin(wt)\). Let \(v_m\) be maximum speed of the body and \(v_\text{avg}\) be average speed of the body in one complete oscillation. If the ratio of \(v_m:v_\text{avg}\) is given by \(\dfrac{\pi}{a}\), then find the value of \(a^2-7a+10\).

Details and Assumptions:

  • Take time period of one complete oscillation, \(T=\dfrac{2\pi}{w}\).

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