1. PHY221 Ch21: SHM 1.Main Points: Spring force and simple harmonic motion in 1d General solution a Cos  t+  Plot x, v, a 2.Example Vertical spring with mass and oscillation around equilibrium Why are springs important: Systems close to equilibrium

2. PHY221 Ch21: SHM 1. Main Points 1.1 Spring force and simple harmonic motion in 1d

3. PHY221 Ch21: SHM 1. Main Points 1.1 Spring force and simple harmonic motion in 1d

4. PHY221 Ch21: SHM 1. Main Points 1.2 General solution a Cos  t+ 

5. PHY221 Ch21: SHM 1. Main Points 1.3 Plot x, v, a

6. PHY221 Ch21: SHM 2. Examples 2.1 Vertical spring with mass and oscillation around equilibrium Now let’s look at a spring and mass m hanging from, say, the ceiling:

7. PHY221 Ch21: SHM 2. Examples 2.2 Why are springs important (cont’d) Comment on Taylor series expansion: a. Preliminaries: quadratic approximation of a function U(x) around a value x e

8. PHY221 Ch21: SHM 2. Examples 2.2 Why are springs important: Systems close to equilibrium

9. PHY221 Ch21: SHM 2. Examples 2.1 Vertical spring with mass and oscillation around equilibrium