Oct15-06, 02:12 PM
A particle of mass m is moving under the ocmbined action of the forces -kx, a damping force -2mb (dx/dt) and a driving force Ft. Express the solutions in terms of intial position x(t=0) and the initial velocity of the particle.
For the complementary solution, use x(t) = e^(-bt) A sin (w1t + theta)
And the for the particular solution, use Ct + D
w1^2 = w0^2 - b^2 w0^2 = k/m
Here's what I have so far:
m (dx^2/dt^2) + 2mb (dx/dt) + kx = Ft
(dx^2/dt^2) + 2b (dx/dt) + w0^2 x = At (A = F/m)
The complementary solution is x = e^(-bt) (A1e^(w1t) + A2e^-(w1t). I dont know how to convert this to the form above. And I am totally clueless as to how to find the particular solution.
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