
#1
Oct1506, 02:12 PM

P: 8

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. Please help! 


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