Wednesday, January 7, 2015

Chapter SHM Example01


Loo Kang WEE, Tat Leong LEE & Giam Hwee GOH

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

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

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_{theory} = 2 \pi \sqrt {\frac{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 \frac{m}{s^{2}}$
  3. A suggested record of the results could look like this
    Angle / degree
    T / s
    T _theory / s
    Error = (T-T_theory)/T*100  / %
    5



    10



    15



    20



    30



    40



    50



    60



    70



    80



    90



  4. With the evidences, suggests what the conditions of which the angle of oscillation can the actual period T be approximated to theoretical period such that $ T \approx T_{theory} = 2 \pi \sqrt {\frac{L}{g}}$

Suggested Answer 1:

 $ \theta  \approx 10 $ degrees for error of  $ \frac {2.010-2.006}{2.010}= 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.

Other Interesting fact(s):

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