Damped Free Vibration

",--_m __ 1: k,-X....i.-m_t .... c..,x

the equation of motion becomes

mx = -c .. 'c - kx

which, on rearranging, takes the form

mx + ex + kx = 0

Spring force = kx

D . f dx ampmg orce = e-dt

d2 x Inertia force = m-..,

dto.

For the trial solution of the homogeneous equation, let

x= Celt

x=,ce# .i=rCe."