1. Simple Harmonic Motion

2. SHM Position, Velocity, and Acceleration

3. Springs and Simple Harmonic Motion

4. Equations of Motion
Conservation of Energy allows a calculation of the velocity of the object at any position in its motion…

5. Energy in SHM Energy-time graphs velocity energy KE PE Total
Note: For a spring-mass system:
KE = ½ mv2  KE is zero when v = 0
PE = ½ kx2  PE is zero when x = 0 (i.e. at vmax)

6. Energy–displacement graphs
+xo
-xo KE PE
Total
Note: For a spring-mass system:
KE = ½ mv2  KE is zero when v = 0 (i.e. at xo)
PE = ½ kx2  PE is zero when x = 0

7. Conservation of Energy For A Spring in Horizontal Motion
E = Kinetic Elastic Potential
E = ½ mv ½ kx = Constant
At maximum displacement, velocity is zero and all energy is elastic potential,
so total energy is equal to
½ kxo2

8. Simple Harmonic Motion - Energy
Ek (max) = 1/2mvo2
Ep (max) = 1/2kxo2
Where they happen
Ek: max
Ep: max max

9. Potential energy in SHM
If a = - ω2x
then the average force applied trying to pull the object back to the equilibrium position as it moves away from the equilibrium position is…
F = - ½ mω2x
Work done by this force must equal the PE it gains (e.g in the springs being stretched). Thus..
Ep (max) = ½ mω2xo2