Conservation of energy

work your d to something from defined zero GPE to somewhere else.
Elastic PE = work you did to stetch the spring from unstreched.

verify conservation of energy in mass-spring system.
things for measure.
1. KE of mass get v from motion sensor.
2. GPE of the mass get mass
3.Elastic PE of the spring =1/2k(stretch)^2
 k= hang a mass get streach
4/ GPE of the spring (uniform spring)

GPE of spring is constant +mgy/2

5. KE of spring choose respresent piece of mass

d(KE) of the bit=(dm/2)v^2=(1/2)*dm((g/L)*Vend)^2=(1/2)(M/L)*dy*((y/L)Vend)^2

take the intergal of the d(KE) form 0 to L.

KE=(1/6)M*Vend^2.

Set up the equirement as showen

Measure the mass of the spring is 64g and hanging a mass of 300g.

as the sping is stretched 0.24m find out the sring consitant is 16.33N/m.

Recored the y as the spring hanging the mass with no motion

Recored the data when you lease the mass from a stretched positon.

Add new calculation coulumn named "KE m"

=0.5+0.3*"velocity"^2

Add new calculation coulumn named "GPE m"

=0.3*9.8*"position"

Add new calculation coulumn named "PE of the spring"

=0.5*0.064*9.8*"position"

Add new calculation coulumn named "GPE of the spring"

=(1/6)*0.064*"velocity"^2

Add new calculation coulumn named "KE of spring"

=0.5*0.064*"velocity"^2

Add new calculation coulumn named Total energy

="KE m"+"GPE m"+"PE of the spring"+"GPE of the spring"+"KE of spring"

 Add the Total energy in the graph
As it shown below it looks like a horizontal line which can verify the total energy is conserved.