1. Simple pendulum Physical pendulum Diatomic molecule Damped oscillations Driven oscillations Lecture 24: General Oscillations

2. SHO Equation for SHO General solution:

3. Simple Pendulum

4. T does not produce a torque, since the line of action goes through point P

5. Simple pendulum oscillations Differential equation of simple harmonic oscillator Demo: Simple pendulum with different masses, lengths and amplitudes

6. Period independent of mass Period independent of amplitude

7. Physical Pendulum SHO

8. Motion of the Physical Pendulum SHO Demo: Meter stick pivoted at different positions I is moment of inertia about axis P D is distance between P and CM Parallel axis theorem:

10. Example A vertical rod of mass M and length L can freely oscillate about a pivot P located at the top end. A small sphere of mass M is rigidly attached to the bottom end. The sphere can be considered a point mass. What is the period of small oscillations for this system?

11. Example A uniform disk of mass M and radius R is pivoted at a point at the rim. Find the period for small oscillations.

12. Vibrations of Molecules Diatomic molecule: two atoms separated a distance r

13. Diatomic molecule near equilibrium

15. Damped Oscillations

16. Characteristics of damped oscillation

17. Driven oscillations http://www.walter-fendt.de/ph14e/resonance.htm

18. Resonance http://www.walter-fendt.de/ph14e/resonance.htm If driving frequency close to natural frequency catastrophic growth of amplitude = Resonance

19. Millennium Bridge, London Video: Spontaneous resonance

20. Tacoma Narrows Bridge Collapse Cause still disputed, not technically resonance – but the video is worth watching and fits very well here