Conservation of Energy with an Oscillating Mass on a Spring

Purpose: In this lab we show the the conservation of energy in a system consisting of a mass hanging on a spring. To do this we will need to measure the kinetic energy of the mass, kinetic energy of the spring, potential energy of the mass, potential energy of the spring, the elastic energy in the spring, gravitational potential energy of the spring, and finally the total of all the energies listed above.


Experiment: For this we need a spring with a mass attached to one end and fixed to another point. We place a sensor below the mass to capture the motion of the mass-spring system. We first have to calculate a spring constant to use in our equations. We used mg=kx where m is the mass of the spring and x is the displacement of the spring.

We first had to calculate the individual energies within the system which would give us the total energy. As you can see in the pictures above and below, we found the PE, KE and  SpringPE

In the picture above, we have the total energy in the system which can be shown in 5 different equtions: KE of the mass, PE of the mass, Elastic PE of the Spring, KE of the spring and the GPE of the spring. Position data from the experiment would be used to calculate GPE and Elastic PE while velociity would be used to calculate the KE in the system

 

Above we have a picture of our setup using a spring and a mass hanging from the end. We places a motion sensor at the bottom to record the motion of the mass and get our data chart below

Here we have the data that was collected and placed all together on this graph. as you can see, the total energy in the system was conserved, thus proving our theory that all energy is conserved in this system. the different colored lines each represent a type of energy and go as follows
Orange: Total Energy in system
Purple: Potential Energy of the mass
Red: Elastic Potential energy of the Spring
Green: Potential Energy of the Spring
Yellow/Orange: Kinetic Energy of mass
Blue: Kinetic Energy of the spring