1. 4.6c Measuring SHM and Spring Constants horizontally
It is possible to measure the spring constant of a spring or series of springs by mounting them horizontally to a trolley or glider on an air track. By measuring the periods of oscillation and plotting a graph of T2 vs m you should be able to calculate the spring constant.
This can be verified by a simple Hookes law experiment done quickly afterwards where you plot Load (in Newtons) against Extension, the spring constant will be the Gradient of the line.

2. The springs should have some tension in them before you move the trolley to one side and begin the oscillations.
Time the oscillations as you know how to, change the mass and repeat until you have sufficient data. Plot a graph of T2 vs m.
Knowing the relationship between Mass and Period you should be able to work out a value for the spring constant from the gradient of the graph.

3. e e x + F = k(e + x) F = k(e - x)
This means that there is a restoring force initially on the springs of “ke” where the springs have been stretched.
If the trolley is then moved a distance “x” to one side and set oscillating the net force is now “k(e-x)” or “k(e+x)” depending on which side you consider.
This experiment is fundamentally simple but you should be able to see that the restoring force in the springs is “2kx” not “kx” as expected.
Now prove the net force is “2kx”! e e x +
F = k(e + x)
F = k(e - x)

4. F = k(e + x)
F = k(e - x)
So the net force is to the left:
F = k(e + x) - k(e - x)
F = ke + kx - ke + kx
Therefore F = 2kx
This should make sense really because you are using two “springs”.