Can u average (sine)ing function?

Calculus Level 4

A body is executing 1D motion along the yy-axis. It's displacement as a function of time is given by y=Asin(wt)y=A\sin(wt). Let vmv_m be maximum speed of the body and vavgv_\text{avg} be average speed of the body in one complete oscillation. If the ratio of vm:vavgv_m:v_\text{avg} is given by πa\dfrac{\pi}{a}, then find the value of a27a+10a^2-7a+10.

Details and Assumptions:

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

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