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 Ttheory=2πLg−−√ 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=9.81ms2
  3. A suggested record of the results could look like this

  4. Angle / degree

    T / s

    T _theory / s

    Error = (T-T_theory)/T*100 / %

    5




    10




    15




    20




    30




    40




    50




    60




    70




    80




    90




  5. 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≈Ttheory=2πLg−−√

Suggested Answer 1:

θ≈10 degrees for error of 2.010−2.0062.010=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.