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Math Help - Mass-Spring System Beats and Resonance

  1. #1
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    Mass-Spring System Beats and Resonance

    In the Beat not have friction force, correct ?

    m \frac{d^2x}{dt^2} + kx = F_o cos(wt)

    We can write as

    \frac{d^2x}{dt^2} + w_o^2 x = \frac{F_o}{m} cos(wt)

    If w \not= w_o

    Assuming (Particular solution)
    x_p = acos(wt) + bsin(wt)
    Why we have assuming this ?


    How find a(w_o^2 - w^2)cos(wt) + b(w_o^2 - w^2)sin(wt) = \frac{F_o}{m} cos(wt) ???

    And why find that x_p = \frac{F_o}{m(w_o^2 -w^2)}cos(wt) ??
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  2. #2
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    In the equation

    \frac{d^2x}{dt^2} + w_o^2 x = \frac{F_o}{m} cos(wt)

    w_o is the frequency of oscillation of the system and w is frequency of oscillation of the external force ???
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