Grade 11Wave Motion
Starting from Eq. 17-43, find the velocity vx (= dx/dt) in forced oscillatory motion. Show that the velocity amplitude is vm = Fm/[(mω’' – k/ω’')2 + b2]1/2. The equations of Section 17-8 are identical in form with those representing an electrical circuit containing a resistance R, and inductance L, and a capacitance C in series with an alternating emf V = Vm cos oω’’t. Hence b, m, k, and Fm, are analogous to R, L, 1/C, and Vm s respectively, and x and v are analogous to electric charge q and current i, respectively. In the electrical case the current amplitude im, analogous to the velocity amplitude vm above, is used to describe the quality of the resonance.
Starting from Eq. 17-43, find the velocity vx (= dx/dt) in forced oscillatory motion. Show that the velocity amplitude is vm = Fm/[(mω’' – k/ω’')2 + b2]1/2. The equations of Section 17-8 are identical in form with those representing an electrical circuit containing a resistance R, and inductance L, and a capacitance C in series with an alternating emf V = Vm cos oω’’t. Hence b, m, k, and Fm, are analogous to R, L, 1/C, and Vm s respectively, and x and v are analogous to electric charge q and current i, respectively. In the electrical case the current amplitude im, analogous to the velocity amplitude vm above, is used to describe the quality of the resonance.
