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phys2
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Homework Statement
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?)
Homework Equations
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!