Problem $1$:

A $12$ inch wrench is attached to the hub of the wheel and extends horizontally, as indicated. After a tool suddenly falls and strikes the free end of the wrench, the wheel is observed to oscillate at its natural frequency with an amplitude of $0\mathrm{.}15$ radians and a period of $0\mathrm{.}1$ seconds. Determine the impulse imparted by the tool. $($the wheel is connected to long axle that is supported by a fixed frictionless collar$),$ Use: $I=\frac{1}{2}m{R}^2$ where $m=20Ib$&$R=15$ inches