2: Forced Oscillation and Resonance

The Physics of Waves · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    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 oscillations. 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.
    4. We study in detail a specific system of a mass on a spring in a viscous fluid. We give a physical explanation of the phase relation between the forcing term and the damping.

    This page titled 2: Forced Oscillation and Resonance was last modified on Mon, 02 Aug 2021 21:34:24 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Howard Georgi via source content that was edited to the style and standards of the LibreTexts platform.