1. The problem statement, all variables and given/known data A physical system is designed having the following equation of motion md2x/dt2 + c(dx/dt) - kx = 0. (a) From the corresponding subsidiary equation, find the solution to this equation of motion. (HINT: use the solution of the damped harmonic oscillator as a guide). (b) How many distinct types of solution and hence physical behaviour does it exhibit ( does it have solutions that correspond to underdamping, overdamping, critical damping?) 2. Relevant equations 3. The attempt at a solution From the hint, I expect the solutions to the system to be similar to the damped solution. So the damped solution was x = -β +- √ (β2 - ω2 ) β = c/m and ω2 = k/m So now I am stuck! Anyone care to point me in the right direction? Thanks!