$(50$ pts$)$ The system dynamics for a spacecraft platform is governed by the following dynamics:

$\frac{d^2}{d{t}^2}p(t)+2\frac{d}{dt}p(t)+4p(t)=(t)$

where $p(t)$ is the actual spacecraft platform position and $(t)$ is the control input thruster angle position. NASA commands a desired platform position $r(t).$ The control amplifier on the spacecraft creates a voltage proportional to the difference between the desired and actual platform position, $v(t)=r(t)-p(t).$ The thruster then responds to this error signal as $\frac{d}{dt}(t)=Kv(t).$ Draw a block diagram of the system. Solve for the characteristic equation governing the transient response from the desired position to the actual position.