# 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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