Physics 8.03 Vibrations and Waves

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Presentation transcript:

Physics 8.03 Vibrations and Waves Lecture 3 HARMONICALLY DRIVEN DAMPED HARMONIC OSCILLATOR

Announcements for today Problem Set 1 Don’t do problem 1.4 (c). New version reflects this change Pick up take-home experiment kits this week Today between 2:00pm and 4:00pm in Room 4-335 Office hours for Nergis Thursday, 2 to 4pm in room 4-338 Tutoring hours Wednesday, 4:00 to 5:00pm in room 4-344 Thursday, 5:00 to 8:00pm in room 8-302

Last time: Damped harmonic oscillator Equation of Motion Three solutions that depend on size of damping Damping slows down natural frequency of oscillator (or makes it stop oscillating altogether) Underdamped Critically damped Overdamped

Today: DRIVEN HARMONIC MOTION Add driving force term to equation of motion Effect Oscillator loses it’s own identity and oscillates at the frequency at which it is driven (not it’s own natural frequency) Mathematical solution Amplitude of oscillation depends on driving frequency Phase of oscillation (relative to driving force) also depends on driving frequency When driving frequency = natural frequency Examples  shattering a wine glass with sound RESONANCE!

Next time: Transient behavior What happens when driving force is first turned on? Transients We started with a second order diff. eqn. so we should get two constants of integration. Where are they? Complete solution to the diff. eqn. includes the homogeneous solution (we got that today) AND a particular solution (that describes the transient behavior of the driven oscillator)