Energy of Simple Harmonic Motion


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.





1. Prepare the equipment for data collection: 2. Carry out the data collection:
3. After analyzing the data, repeat the procedure using a new hanging mass or a new sprin g.



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.