Download presentation

Presentation is loading. Please wait.

1
**Simple Harmonic Motion**

2
**What is an Oscillation? Vibration**

Goes back and forth without any resulting movement SHM - Simple Harmonic Motion

3
**An object in SHM oscillates about a fixed point.**

This fixed point is called mean position, or equilibrium position This is the point where the object would come to rest if no external forces acted on it

4
**Describe restoring force**

Restoring force, and therefore acceleration, is proportional to the displacement from mean position and directed toward it

5
**Examples of SHM: Simple pendulum Mass on a spring Bungee jumping**

Diving board Object bobbing in the water Earthquakes Musical instruments

6
Simple Pendululm Equation: Time is independent of amplitude or mass

7
**Assumptions: 1. Mass of string is negligible compared to mass of load**

2. Friction is negligible 3. Angle of swing is small 4. Gravitational acceleration is constant 5. Length is constant

8
**Mass on a Spring Time is independent gravitational acceleration**

Equation: Time is independent gravitational acceleration

9
**Assumptions: 1. Mass of spring is negligible compared to mass of load**

2. Friction is negligible 3. Spring obeys Hooke’s Law at all times 4. Gravitational acceleration is constant 5. Fixed end of spring can’t move

10
**Restoring Force is proportional to (-) displacement**

Sketch: Negative sign means force is in the opposite direction of the displacement

11
**Variables for SHM: x displacement from mean position**

A maximum displacement (amplitude) Ø phase angle (initial displacement at t = 0) T period (time for one oscillation) f frequency (number of oscillations per unit time) angular frequency

12
**Relationships between variables**

13
Other relationships:

14
Diagrams

15
Graphs:http://physics.bu.edu/~duffy/semester1/c18_SHM_graphs.html

17
**Kinetic and Potential Energies in SHM**

since

19
Damping Energy losses (energy dissipation) due to friction - removes energy from system For an oscillating object with no damping, total energy is constant - depends on mass, square of initial amplitude, angular frequency

20
Damping (continued) Amplitude decreases exponentially - all energy is eventually converted to heat Critical damping (controlled)- oscillations die out in shortest time possible

22
Resonance System displaced from equilibrium position will vibrate at its natural frequency System can be forced to vibrate with a driving force at the natural frequency Examples: musical instruments, machinery, glass, microwave, tuning a radio

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google