Tuesday, January 13, 2015

SHM Chapter 01b pendulum SHM?

Chapter SHM Example 01_02

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?

Example 1: Simple pendulum A pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion

Suggested Inquiry Steps:

  1.     Define the question in your own words
  2.     Plan an investigation to explore angle of release to record the actual period T and theoretical period  T t h e or y = 2 π L g   where L is the length of the mass pendulum of mass, m and g is the gravitational acceleration of which the mass is experiencing, on Earth's surface  g = 9.81 m/s2
  3.     A suggested record of the results could look like this
   
angle / degree T /s  Ttheory / s e r r or = ( T - T t h e or y ) T 100 %
05


10


15


20


30


40


50


60


70


80


90


 
        With the evidences collected or otherwise, suggests what the conditions of which the angle of oscillation can the actual period T be approximated to theoretical period such that  T  ≈  T t h e or y = 2 π L g

Suggested Answer 1:


 angle θ  ≈ 10 degrees for e r r or = ( 2.010 - 2.006 ) 2.010 ( 100 ) = 0.2 % , depending on what is the error acceptable, small angle is typically about less than 10 degree of swing from the vertical.

Conclusion:


Motion approximates simple harmonic motion when the angle of oscillation is small < 10 degrees..

Other Interesting fact(s):


Motion approximates SHM when the spring does not exceed limit of proportionality during oscillations.

Real Life Application of Small Angle Approximations:

Astronomical applications of the Small Angle Approximation

Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM01b/SHM01b_Simulation.xhtml