Consider the equation for free mechanical vibration, my'' + by' + ky=0, and assume the motion is overdamped. Suppose y(0) > 0 and y'(0) > 0. Prove that the mass will never mass throught its equilibrium at any positive time.
Really stuck on this question, all i know is for over damped:
b^2 > 4mk
General solution: y(t)=C1e^(r1t) + C2e^(r2t) --> y(0) = C1 + C2 > 0
y'(t)=C1r1e^(r1t) + C2r2e^(r2t) --> y'(0) = C1r1 + C2r2 > 0
Any help with this question would be really appreciated thanks.