Yes, the damping will dissapate energy so the system has its maximum energy at the beginning. Since it is released from rest, it had no initial speed and so no kinetic energy- the initial potential energy is its total energy at that time.
Just wanted to see if my logic was correct in answering the problem below. Max derviation occurs from equilibrium at the initial time because the amount of energy is the highest as seen in the characteristic equation for an overdamped soltuion where b^2-4mk > 0.
The Question: Given that an overdamped spring-mass-damper system is released from rest. Explain why the maximum deviation from equilibrium occurs at the inital time. This is a completely general result.
Yes, the damping will dissapate energy so the system has its maximum energy at the beginning. Since it is released from rest, it had no initial speed and so no kinetic energy- the initial potential energy is its total energy at that time.