Forced vibration.pdfVIP

Forced vibration Objectives 1. Familiar with how to use the torsion pendulum to test the laws of vibration. 2. Explore the amplitude-frequency and phase-frequency characteristics of forced vibration. Apparatus Bohr resonance instrument，control box and flash. Theory BG - type 2 Bohr resonance instrument consists of vibration analyzer, electric control box and flash shown in figure 1. Figure 1 Bohr resonance instrument The motion in which an object is under a continuous and periodic external force is called forced vibration. This kind of force is called compelling force. If the force changes according to a simple harmonic vibration, the steady state of forced vibration is a simple harmonic oscillation. At this point, the amplitude remains constant but is relevant to the frequency of the compelling force, the natural frequency of the original system and the damping coefficient. When an object is in forced emotion, it’s by two forces, restoring force and damping force. Therefore, in steady state, the object displacement, velocity and force has different phase, and there is a phase difference. When the frequency of the system is just the same to the natural frequency, the resonance occurs. In this condition, the amplitude is the maximal and the difference of the phase is 90 °. In the experiment we study the forced vibration with the balance wheel in the elastic torque swing freely and vibrate forced in the electromagnetic damping moment. A number of physical phenomena about oscillation characteristics of mechanical vibration can be visually displayed by the experiment. When the balance wheel of BG - type 2 Bohr resonance instrument is forced by the external torque M = M0cosωt with the air damping and electromagnetic damping (the damping torque is ) , the equation of motion is (3-1) where I is the moment of inertia of the wheel, -kθ stands for the elastic