Question

The displacement, y(m), of a body is damped oscillation is y=2e^-t sin3t.


use product rule to find an equation for the velocty of object if v=dy/dt.

Answer 1

$\dfrac{dy}{dt}=\dfrac{d(2e^{-t})}{dt}\sin3t+2e^{-t}\dfrac{d(\sin3t)}{dt}= -2e^{-t}\sin3t+2e^{-t}\cdot 3\cos3t=2e^{-t}(-\sin 3t+3\cos 3t)$