Lab: Simple Harmonic Motion

Lab: Simple Harmonic Motion

Purpose: 
Predict and verify the period of a semi-circle foam and a isosceles triangle foam oscillating around a certain pivot.

Equipment:
Photo-gate sensor and foam

Experiment:
1. Set up the apparatus as the pictures show.
2. Calculate the Inertia of the semi-circle around the pivot.
3. Get the expression of angular acceleration and omega.
4. Calculate the value of the period.
5. Hanging the semi-circle around the pivot, give a initial push so that the foam oscillate in a small angle. Record the period.
6. Repeat the step with a different pivot and for the triangle.

Calculation:
Center of mass:

 Moment of Inertia:

 Period at the center of the circle

 Period at the middle of the arc length

Triangle:

Result:

Theoretical and actual value:

 Conclusion:
 Theoretical Period at the center of the circle: 0.602s
Actual Period at the center of the circle: 0.5994s

Theoretical Period at the middle of the arc length: 0.59s
Actual Period at the middle of the arc length: 0.5991s

Theoretical Period of the triangle at the apex: 0.691s
Actual Period of the triangle at the apex: 0.69s

We successfully predict and verify the period of a semi-circle foam and a isosceles triangle foam oscillating around a certain pivot.