PHYS 1750: SELECTED TOPICS in PHYSICS
LECTURE 24. Simple Harmonic Motion
| 15.1. | Spring Review: Vertical springs: | ||
| 1. | Total F = kx-mg | ||
| 2. | Equilibrium xo= mg/k | ||
| 3. |
Total F = k (x-xo) In formulae below, all displacements x measured from xo | ||
| 15.2. | Period T vs. Frequency f: f = 1 / T | ||
| 15.3. |
Simple Harmonic Motion:
Periodic, displacement from -X to X; X = Amplitude | ||
| 15.5. | Velocity at Position x | ||
| 1. | Conservation of Energy: | ||
| a. | KE = mv 2 / 2 | ||
| b. | PE = kx 2 / 2 | ||
| c. | TE = kX 2 / 2 | ||
| 2. | v 2 = (X 2-x 2) k / m | ||
| 15.6. |
Uniform Circular Motion | ||
| 1. | Same vx(x) | ||
| 2. | vx = -vosin θ | ||
| 3. | Period T and frequency ω relations: ω = 2π / T | ||
| a. | vo = 2πX / T = ωX | ||
| b. | kX2 / 2 = mvo2 / 2 | ||
| c. | X / vo = sqrt ( m / k) | ||
| d. | ω = sqrt ( k / m) | ||
| A cute applet | |||
| 15.3. | Position, Velocity, Acceleration | ||
| 1. | x = X cos(ωt) | ||
| 2. | v = -X ω sin(ωt) | ||
| 3. | a = -X ω2 cos(ωt) | ||
Review Questions follow next lecture.
Lecture 25: The Pendulum and an Introduction to Waves
