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.

Lab: Spring-Mass Oscillation

Lab: Spring-Mass Oscillation

Purpose:
Find the relationship , between the period and the mass with the same spring and between the period and the spring constant with a constant mass.

Equipment:
Spring. various mass, motion sensor, ruler

Experiment:
1. Set up the apparatus as the pictures show.
2. Hang a 50g mass on the spring and measure the length of the spring L1; Hang a 100g mass on the spring and measure the length of the spring L2
3. Calculate the spring constant based on the mass and the difference of length.
4. Calculate the mass needed to reach the same total mass with other group.
5. Hang the calculated mass on the spring and stretch a little so that the mass oscillates, and record the period.
6. Write down the data from other group, and create a graph of spring constant vs. period with the same mass.
7. Hang different mass on the same spring and record the period for each oscillation.
8. Create a graph of mass vs. period.

Data: 

 Result:

Conclusion:
Graph of Period vs. Mass: y=2.686*x^0.4632
Graph of Period vs. Spring constant: y=2.570*x^-0.5702