Simple Harmonic Motion
Simple harmonic motion (SHM) is the motion of an object subject to a force that is proportional to the object’s displacement. One example of SHM is the motion of a mass attached to a spring. In this case, the relationship between the spring force and the displacement is given by Hooke’s Law, F = -kx, where k is the spring constant, x is the displacement from the equilibrium length of the spring, and the minus sign indicates that the force opposes the displacement. In this laboratory you will study SHM as it applies to a:
1. Mass Attached to a Spring, and
2. Simple Pendulum
Mass Attached to a Spring
The motion of a mass attached to a spring is simple harmonic motion if:
1. there is no friction and
2. if the displacement of the mass from its equilibrium position at x = 0 is “small”. The displacement must be small enough so that the spring is not stretched beyond its elastic limit and becomes distorted.
Materials and equipment: big spring, weight hanger, masses, motion detector, and Logger Pro interface and software.
A) Does the period of the motion depend on the amplitude?
1. Please write down a prediction with a reason for question A.
2. Suspend the spring from the support rod.
3. From the lose end of the spring hang a 50g weight hanger with a 50g mass for a total of 100g.
4. Measure the position of the end of the spring relative to the floor or table top. This will be your spring/mass equilibrium position.
5. Pull the mass below the spring/mass equilibrium position.
6. Release the mass and use the motion detector to record the motion.
7. Use the motion data to determine the period of the motion. Describe how you used this data to determine the period.
8. How is the amplitude defined for this motion?
9. Repeat this procedure for five additional amplitudes. Record the amplitudes and the periods in a table.
10. Does your data indicate that the period of motion depends on the amplitude? Support your answer.
11. Theoretically (according to the equations), does the period of the motion depend on the amplitude? Support your answer.
B) Does the period of the motion depend on the mass?
1. Please write down a prediction with a reason for question B
2. Experimentally determine the periods of motion for six masses 50g, 100g, 150g, 200g, 250g and 300g. Record the mass and the corresponding period in a table.