# 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, $$T=\dfrac{2\pi}{w}$$.