1. Simple Harmonic Motion

2. Springs The force from a spring depends on the mass
The greater the mass,
The greater the spring force

3. Hooke’s law F = - k x F is force (N) k is the spring constant (N/m)
“The magnitude of the force exerted by a spring is equal to the spring constant times the distance the spring is stretched or compressed from its equilibrium position”
F = - k x
F is force (N)
k is the spring constant (N/m)
x is the distance from equilibrium (m)
Why “-”? Because the force is in the opposite direction that the spring is being stretched!

4. F = -kx2
PEsp= ½kx2
Warm up
A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end.
Determine the spring constant
How much elastic potential energy does the spring have when it is stretched this far?

5. Periodic Motion Motion that repeats in a regular cycle
Mass on a spring
Vibrating guitar string
Tree swaying in the wind
Equilibrium Position- where the net force on the object is zero
All other positions, there is a force working to bring the object back to equilibrium

6. Periodic Motion
Period (T) – amount of time needed for an object to complete one cycle of motion
Amplitude – the maximum distance the object is from the equilibrium point

7. Simple harmonic motion
When a force acting to restore an object is directly proportional to the displacement of the object
Ex: The force exerted by a spring is
proportional to how far the spring is stretched

8. Hooke’s law
F = - k x
The force from the spring changes depending on the displacement
PEspring = ½kx2
KE + PE = ME

9. Mass on a spring interactive

10. Mass on a spring

11. Mass on a spring and energy
Where is there maximum potential energy?
Where is there maximum kinetic energy?
Max Potential: top and bottom of range of motion
Max Kinetic: at equilibrium position

12. Energy distribution through range of motion (Page 384 of your textbook