Oscillations

Oscillations PowerPoint PPT Presentation


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2. What will we do in this chapter?. This is the first of several lectures on the the harmonic oscillator. We begin by reviewing our previous solution for SHM and use similar techniques to solve for a simple pendulum. We next solve the SHM using the auxiliary equation technique from linear different

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Oscillations

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1. 1 Oscillations SHM review Analogy with simple pendulum SHM using differential equations Auxiliary Equation Complex solutions Forcing a real solution The damped harmonic oscillator Equation of motion Auxiliary equation Three damping cases Under damping General solution Over damping General solution Solution in terms of initial conditions Critical Damping Break down of auxiliary equation method and how to fix it General solution Solution in terms of initial conditions Over damping as ideal damping Phase diagrams Un-damped phase diagram Obtaining phase equations directly The under-damped logarithmic spiral Critical damping example Harmonic oscillations in two dimensions Lissajous figures

2. 2 What will we do in this chapter?

3. 3 Simple harmonic motion

4. 4 SHM solution by DE methods

5. 5 DE methods (continued)

6. 6 Damping cases

7. 7 An under-damped case

8. 8 Over damped case

9. 9 Critical damping

10. 10 Example of Critical Damping

11. 11 Phase Diagram

12. 12 Phase Diagrams (continued)

13. 13 Critically damped phase diagram

14. 14 Harmonic motion in two directions

15. 15 Lissajou figure with unequal frequency

16. 16 A cool trig identity

17. 17 Lissajous figures with different frequencies

18. 18 Lissajous with irrational frequency ratios

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