Question

Please show what basic mechanical equations are used or explain how to derive the equation. Not just looking for the answer.

c 60 kg/s is subject to a A damped harmonic oscillator with m - 10 kg, k 250 N/m, and driving force given by Fo cos ot, where Fo 48 N. (a) What value of ω results in steady-state oscillations with maximum amplitude? Under th condition:

Answer 1

"Periodically forced Harmonic oscillator We mean the linear second order non-Homogeneous differential eqn my"" + by' + ky = F cos (wt) where m > 0, b > 0, k > 0, b-is damping coefficient, b = 0 (undamped case) b > 0 (damped case) undamped (b = 0) my"" + ky = F cos (wt) (2) w_0 = squareroot k/m This is natural frequency of the undamped, unforced harmonic oscillator solve (2), we consider w notequalto w_0, w = w_0 case w notequalto w_0 than solution of equ (2) is y (t) = c_1 cos (w, t) + c_2 sin (w_0 t) + F/m(w^2 - w^2_1) cos (wt) m (w^2 - w^2_1) if w = w_0 than case of Resonance after solving this we find -2m w_0 A sin (w_0 t) + 2 m w_0 B Cos (w_0 t) = F cos (w_0 t) \r\n I use the convention rightarrow b instead of C given that"