Savchenko Problem 3.5.27

Physics · mechanics · electromagnetism

Problem

If the weights of the pendulums are equally deflected to one side and released, the system will vibrate with frequency ω1\omega_1 = g/l\sqrt{g/l}. If, however, they are deflected by an equal distance in opposite directions, the system will vibrate with the frequency ω2\omega_2 = g/l+2k/m\sqrt{g/l+2k/m}. In general, the motion of the weights is the result of the superposition of these oscillations: x1x_1 = B cos(ω1t+φ\omega_1 t+\varphi) + A cos ω0t\omega_0 t, x2x_2 = B cos(ω1t+φ\omega_1 t+\varphi) − A cos ω0t\omega_0 t. Now, considering the force F cos ω0t\omega_0 t acting on the left weight from the side of the spring as a forcing force, determine the value of A through the parameters F, m, ω0\omega_0 and ω1\omega_1. The term B cos(ω1t+φ\omega_1 t+\varphi) represents the free oscillation of the isolated oscillator. What determines the choice of parameters B and φ\varphi?

Browse the problem library