Energy in Simple Harmonic Motion - Ryerson Department of Physics

PCS125 Experiment 2 – The Simple Harmonic Motion
7. Predict what would happen to the plot of the model if you doubled the parameter for A by
sketching both the current model and the new model with doubled A. Now double the parameter
for A in the manual fit dialog box to compare to your prediction.
8. Similarly, predict how the model plot would change if you doubled f, and then check by
modifying the model definition.
9. Click , and optionally print your graph.
EXTENSIONS
1. Investigate how changing the spring amplitude changes the period of the motion. Take care not
to use too large amplitude so that the mass does not come closer than 40 cm to the detector or
fall from the spring.
2. How will damping change the data Tape an index card to the bottom of the mass and collect
additional data. You may want to take data for about 2 minutes. Does the model still fit well in
this case
3. Describe how would you have to extend this experiment to discover the relationship between the
mass attached to the spring and the period of his motion.
PART II: ENERGY IN SHM
We can describe an oscillating mass in terms of its position, velocity, and acceleration as a function
of time. We can also describe the system from an energy perspective. In this experiment, you will
measure the position and velocity as a function of time for an oscillating mass and spring system,
and from those data, plot the kinetic and potential energies of the system.
Energy is present in three forms for the mass and spring system. The mass m, with velocity v, can
have kinetic energy KE
The spring can hold elastic potential energy, or PE elastic . We calculate PE elastic by using
where k is the spring constant and y is the extension or compression of the spring measured from the
equilibrium position.
The mass and spring system also has gravitational potential energy (PE gravitational = mgy), but we do
not have to include the gravitational potential energy term if we measure the spring length from the
hanging equilibrium position. We can then concentrate on the exchange of energy between kinetic
energy and elastic potential energy.
If there are no other forces experienced by the system, then the principle of conservation of energy
tells us that the sum ΔKE + ΔPE elastic = 0, which we can test experimentally.
OBJECTIVES
• Examine the energies involved in simple harmonic motion.
• Test the principle of conservation of energy.
MATERIALS
computer
Vernier computer interface
slotted mass set, 50 g to 300 g in 50 g steps
slotted mass hanger