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A simple harmonic oscillator, of mass m and natural frequency ωo, experiences an oscillating driving force f(t)=m a cos(ωt). Therefore, its equation of motion is
d2x/dt2 + ωo2x =αcos(ωt)
where x is the position. Given that at t=0 we have x=dx/dt=0, find the function x(t). Use BOTH with variation of the parameters and guessing methods. Describe the solution if ω is approximately, but not exactly, equal to ωo. Give an example of a physical system where this happens.
The leg and cast weigh 290 -N, with the center of mass as indicated by the blue arrow in the diagram. The counterbalance w2 weighs 120 N. Determine the weight w1 and angle α needed in order that there is no force exerted on the hip joint by the le..
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