1 / 11

THIS LECTURE

THIS LECTURE. Damped oscillators: energy versus time. From damped to driven oscillators. Driven oscillator: an oscillator driven by an external force. Light damping. Critical damping. A. Heavy damping. Damped oscillator. Newton equation of motion. g = coeff. of damping.

oren-fitzgerald
Download Presentation

THIS LECTURE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. THIS LECTURE • Damped oscillators: energy versus time • From damped to driven oscillators Driven oscillator: an oscillator driven by an external force

  2. Light damping Critical damping A Heavy damping Damped oscillator Newton equation of motion g= coeff. of damping w0 = natural ang. frequency Three different dependencies of x on t

  3. Damped oscillator Newton equation of motion g= coeff. of damping w0 = natural ang. frequency Three different dependencies of x on t For heavy, light and critical damping

  4. Quality factor, Q Q can be also expressed in terms of |DE|/E |DE|/E = fractional energy loss per cycle

  5. Problem on Q-factor: After an earthquake, the Earth can ring for up two months! If the Earth has a Q-factor of 100, calculate the percentage of energy loss per vibration. We use to derive

  6. Driven oscillators Oscillators driven by external forces Driving force, F F induces a displacement, x Resonance When the frequency, w, of the driving force matches the natural angular frequency, w0, of the mass on the spring, the motion is amplified.

  7. Driven oscillators Millennium Bridge (London)

  8. Driving force Equation of motion x Solution x=x1+x2 t Transient motion x=x1+x2 Steady-state motion x~ x2 PREVIOUS LECTURE Driven oscillators A0 and j depend on w

  9. Steady state solution Driven oscillators To find A0 and j 1) we use complex notation • Equation of motion in complex form 2) we use method of differentiation and substitution A0 and j depend on w

  10. Magnitude of displacement: A0 A0 Magnitude of velocity: wA0 0 w w A0 0 w

  11. Bridges Man in the bathtub Atoms and molecules Driving force: light,... Driving force: wind,... Resonance Characteristic resonance frequencies • >> 1 Hz Atoms • << 1 Hz Bridges u ~1 Hz

More Related