(Solved): 3 A damped oscillator A damped oscillator obeys the following differential equation: dt2d2y+cdt ...

3 A damped oscillator A damped oscillator obeys the following differential equation: $$\frac{d^{2}y}{d{t}^2}+c\frac{dy}{dt}+2y=0$$ where $$c$$ is defined as a positive constant. a. The general solution to the differential equation is $$A{e}^{p_{1}t}+B{e}^{p_2}t$$ where $$p_1$$ and $$p_2$$ are the roots of the quadratic equation $$p^2+cp+2=0$$. Find the general solution to the differential equation if the damping constant $$c=2$$. b. How large would $$c$$ have to be in order for the oscillator to be overdamped, meaning it would decay exponentially without oscillating?