SHM Chapter 01 intro pendulum

Simple Harmonic Motion

Simple Harmonic Motion

Learning Outcomes (LOs)

1. describe simple examples of free oscillations.
2. investigate the motion of an oscillator using experimental and graphical methods.
3. understand and use the terms amplitude, period, frequency and angular frequency.
4. recognise and use the equation a =  - ω² x as the defining equation of simple harmonic motion.
5. recall and use x= x₀ ω sin( ωt )as a solution to the equation a =  - ω² x
6. recognise and use v = v₀ cos ( ω t )  , ${\displaystyle v=\pm \omega \sqrt{(x_0^2-x^2)}}$
7. describe with graphical illustrations, the changes in displacement, velocity and acceleration during simple harmonic motion.
8. describe the interchange between kinetic and potential energy during simple harmonic motion.
9. describe practical examples of damped oscillations with particular reference to the effects of the degree of damping and the importance of critical damping in cases such as a car suspension system.
10. describe practical examples of forced oscillations and resonance.
11. show an appreciation that there are some circumstances in which resonance is useful and other circumstances in which resonance should be avoided.
12. describe graphically how the amplitude of a forced oscillation changes with frequency near to the natural frequency of the system, and understand qualitatively the factors which determine the frequency response and sharpness of the resonance.

Simple examples of free oscillations LO(a)

static picture of a pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion 

Example 1: Simple pendulum

dynamic picture of a pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion

dynamic picture of a pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion

Run Model: 

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM01/SHM01_Simulation.xhtml

Q1: what is the maximum angle of release before the motion is not accurately described as a simple harmonic motion for the case of a simple free pendulum?
A1: : 10 degrees for error of , depending on what is the error acceptable, small angle is typically about less than 10 degree of swing from the vertical.