1. -Simple Pendulum -Damped and Forced Oscillations -Resonance AP Physics C Mrs. Coyle Mrs. Coyle

2. Objectives Simple Pendulum as SHM Period of a Simple Pendulum Damped Oscillations-graphs Resonance- Graphs

3. Review: The acceleration in SHM is not constant. It is proportional to – x. To prove if a motion is SHM, you must show that the acceleration is proportional to –x. The coefficient of x is w 2. To prove if a motion is SHM, you must show that the acceleration is proportional to –x. The coefficient of x is w 2. http://www.physics.byu.edu/research/acous tics/animationsSHO.aspx

4. The Simple Pendulum The motion of a simple pendulum is very close to a SHM oscillator, i f the angle is <10 o http://phys.columbia.edu/~tutorial/estimation /tut_e_2_3.html

5. Angular Quantities s=  r v=  r a  r

6.  Radial:  F=T-mgcos  =0

8. Characteristics of the Simple Pendulum Angular position:  =  max cos (  t) Angular frequency: Period:

9. Question 2: Does mass affect the period of the pendulum? Question 1: If a pendulum was taken to a planet where the acceleration due to gravity was four times that of g on the earth, how would the period change? See the University of Colorado Simulation Period of the Simple Pendulum

10. Damped Oscillations Non conservative forces are present (ex: friction, resistive forces). The amplitude and thus the mechanical energy is reduced over time.

11. Types of Damping A.Underdamped B.Critically damped the system will not oscillate (quick return to equilibrium). C.Overdamped return to equilibrium without oscillation.

12. Forced vibrations: when an external force causes a system to oscillate External Force

13. How can a damped system have an undamped motion (no decrease in amplitude)? To compensate for the loss of mechanical energy due to the resistive force, apply a forced vibration of equal energy.

14. Resonance: increase in amplitude due to addition of an external force. When the frequency of the driving force is near the natural frequency (    ) an increase in amplitude occurs The natural frequency   is also called the resonance frequency of the system

15. Takoma Narrows Bridge: collapses in November, 1940, under 42mph winds (opened in July 1940)

16. Summary Simple Pendulum as SHM- small angles Period of a Simple Pendulum- Damped Oscillations-graphs Resonance- Graphs