Energy of Simple Harmonic Motion
ENERGY OF A SPRING/MASS
When a mass is connected gently to a hanging spring, it moves downward until it reaches an equilibrium position. When it
is displaced upwards or downwards from that point, it goes into Simple Harmonic Motion (SHM).
During SHM, the mass moves upwards and downwards, changing the length of the spring. Three forms of energy are involved in this motion - gravitational poten
tial, translational kinetic and elastic potential. In this lab, you will examine the relationships between these three quantities throughout a single cycle of motion and test the conservation of mechanical energy.
ne a classic physics lab from the standpoint of the energies involved
- Test the conservation of mechanical energy
Spring, Hanging Mass, Motion Sensor, Computer Interface
Computer, Interface Software
- As the mass moves up and down, what energies are involved? How did the mass get the original amount of each energy?
- What relationship gives the amount of elastic energy in the spring?
- Compare the amounts of eac
h energy (in a qualitative way) at the three extremes of motion - topmost point, middle, and bottommost point.
1. Prepare the equipment for data collection:
2. Carry out the data collection:
- Connect the laboratory interface to the computer.
onnect the motion sensor to the appropriate channel of the laboratory interface.
- Record the total mass.
- Position the mass so it hangs 60-70 cm above the motion sensor when it is in equilibrium.
- Launch the software needed for measuring position and velocity during your experiment.
- Pull the mass down approximately 10 cm (if the spring will allow this much extension) and release it, setting it in
- When the motion is smooth and straight up and down, begin data collection.
- Stop the data collection after two or three cycles have elapsed.
3. After analyzing the data, repeat the procedure using a new hanging mass or a new sprin
- Construct a spreadsheet that contains the values of the following quantities:
- Constants: Mass, Spring Constant
- Variables: Position (height), Velocity, Time
- Calculated Values:
Gravitational Potential Energy (Ug)
Kinetic Energy (K)
Elastic Potential Energy (Ue)
Total Mechanical Energy (Et)
- Record the position, velocity and time for at least 15 different positions during a single cycle of the motion.
li> Calculate Ug based on height above the lowest point of the motion.
- Calculate Ue based on distance below the highest point of the motion.
- Graph all four calculated values as functions of time.
- What is your conclusion regarding the total
mechanical energy during a cycle of motion?
- What observations did you make regarding the relative sizes of the various energies during a cycle of motion?
1. If one considers that energy must be conserved, and theref
ore the total energy at each position must be the same, the lab can be re-configured to dynamically determine the spring constant k. What value of k would keep the total energy constant, and how does this agree/disagree with the value of k determi
ned in a separate measurement?
2. An air track glider could be mounted between two springs and set into SHM. A similar analysis could be done, but with only elastic and kinetic energies. If the air track were mounted at an angle, gravitational energ
y would be introduced.
Another alternative would be to fasten the glider to a spring, and connect a mass to it by a thread passing over a pulley. The total mass must be used, and the gravitational potential energy changes of the mass moving up and do
wn must be included.
With springs connected on either side of the glider, the effective spring constant could be determined and related to the individual spring constants. Although this is often a problem for AP students, it can be examined experimen
tally by non-AP students in this format.
Written by Clarence Bakken. Posted 7/29/96.