A mass oscillates on a spring about the point x = 0, and is subject to frictional forces. The velocity of the mass at time t is found to be v(t) = -V∗e^(-at) sin(bt), where V^∗, a and b are all positive constants. Note that positive velocity is de?ned to be in the positive x-direction (i.e. the direction in which x increases).
Use integration by parts to ?nd the position x of the mass at time t, given that x(0) = 1.