## Wednesday, January 7, 2015

### 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.