1. SIMPLE HARMONIC MOTION

2. Simple harmonic motion- Any motion that is defined by period and amplitude
Period- The time for one cycle
T= time/ #cycles
Frequency- cycles per second.
f = #cycles/ time
f=1/T (inverse of the period)

3. Amplitude- Displacement from equilibrium.
Periodic Motion- The acceleration is directly proportional to the displacement of the objects equilibrium position. (vibrations, springs, pendulums and waves)

4. PENDULUM
MOTION

5. Pendulum- Any object that swings back and forth about an axis
T = time/# of swings

6. Period of a pendulum is:
Independent of mass
Independent of release angle
Independent of weight
Dependent only on the length of the pendulum.

7. *SORRY FOLKS- NOT ON THE
FORMULA
T= 2π√ L/g
T-period(sec) L-length (m)
g= 9.81m/s2
*SORRY FOLKS- NOT ON THE
REFERENCE TABLE*

8. Ex: What is the period of a pendulum that is 50cm long?
T= 2π√ L/g
T= 2(3.14)√ 0.50m/9.81m/s2
T= 1.4sec

9. Graphs
period
period
mass
angle
period
length

10. KE and PE
As the pendulum swings from its peak to the center, the potential energy is converted to kinetic energy.

11. GRAPHING THE SWING Displacement of the swing is equal to its amplitude
time
Displacement of the swing is equal to its amplitude

12. MECHANICAL RESONANCE An increase in the amplitude
(displacement) due to an applied force .
POW

13. SPRING MOTION

14. Hooke’s Law
The amount of force acting on a spring is directly proportional to its change in length as long as it doesn’t exceed its elastic limit.

15. Fs = k x Fs –force on spring (N)
x- change in length (m) k- spring constant (N/m)
(spring constant will
vary with each spring)

16. The slope of the line is equal to the spring constant
GRAPH
The slope of the line is equal to the spring constant
Tight spring
F(N)
Loose spring
X (m)
Slope=ΔF/Δx=k

17. ELASTIC POTENTIAL ENERGY
k =N/m PEs- joules
x = m
PE (J)
PES = ½ kx2
x (m)

18. F=mg F= .8kg(9.81m/s2) F= 7.85N F=kx 7.85N = k (0.1m) K= 78.5 N/m
Ex: What is the gain in potential energy of a spring that is stretched 10cm by an 800g mass?
F=mg
F= .8kg(9.81m/s2)
F= 7.85N
F=kx
7.85N = k (0.1m)
K= 78.5 N/m
PEs = 1/2kx2
PEs = ½(78.5N/m)(0.1m)2
PEs = Joules