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Forced Oscillation and Resonance

Chapter 2 Forced Oscillation and Resonance The Forced Oscillation problem will be crucial to our understanding of wave phenomena. Complex exponentials are even more useful for the discussion of damping and Forced oscil-lations. They will help us to discuss Forced oscillations without getting lost in algebra. Preview In this chapter, we apply the tools of complex exponentials and time translation invariance to deal with damped Oscillation and the important physical phenomenon of Resonance in single oscillators. 1. We set up and solve (using complex exponentials) the equation of motion for a damped harmonic oscillator in the overdamped, underdamped and critically damped regions. 2. We set up the equation of motion for the damped and Forced harmonic oscillator. 3. We study the solution, which exhibits a Resonance when the forcing frequency equals the free Oscillation frequency of the corresponding undamped oscillator.

2.1 Damped Oscillators . Consider first the free oscillation of a damped oscillator. This could be, for example, a system . of a block attached to a spring, like that shown in figure 1.1, but with the whole system . immersed in a viscous fluid. Then in addition to the restoring force from the spring, the block . 37

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