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 v_x (= dx/dt) in forced oscillatory motion. Show that the velocity amplitude is v_m = F_m/[(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 = 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.