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Starting from Eq. 17-43, find the velocity v x (= dx/dt) in forced oscillatory motion. Show that the velocity amplitude is v m = F m /[(mω’' – k/ω’') 2 + b 2 ] 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 = V m cos oω’’t. Hence b, m, k, and F m , are analogous to R, L, 1/C, and V m s respectively, and x and v are analogous to electric charge q and current i, respectively. In the electrical case the current amplitude i m , analogous to the velocity amplitude v m 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.

Grade:11

2 Answers

Jitender Pal
askIITians Faculty 365 Points
7 years ago
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pa1
357 Points
7 years ago
img Jitender Pal

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