1. Vibration and waves

2. A restoring force always pushes or pulls the object toward the equilibrium position
Simple harmonic motion -occurs when the net force is proportional to the displacement from the equilibrium point and is always directed toward the equilibrium point

3. The amplitude A – is the maximum distance of the object from its equilibrium position
The period T- is the time it takes the object to move through one compete cycle of motion ( from x=A to x=-A and back to x=A)
The frequency f is the number of complete cycles or vibrations per unit of time (f=1/T)
The harmonic oscillator equation:
a=(-k/m)x
A ranges over the values –kA/m and +kA/m

4. Elastic potential energy: PEs=1/2kx2
Conservation of energy:
(KE +PEg+PEs)i= (KE +PEg+PEs)f

5. Velocity as a Function of position ½ kA2+ 1/2mv2+1/2kx2 v=±√k/m(A2-x2)

6. Comparing harmonic motion with circular motion:
v= C√ (A2-x2)
sinθ=v/vo
sin θ= (√A2-x2)/A
v/vo=(√A2-x2)/A
v= vo(√A2-x2)/A
=C √ (A2-x2)

7. Period and frequency
vo=2πA/T
T=2πA/vo
Conservation of energy1/2kA2=1/2mv2
A/vo =√m/k
T=2π√m/k
f= (1/2π)√k/m
The angular frequency
ω=2πf =√k/m

8. Position, velocity and acceleration as a fct. of time
x=Acosθ
θ =ωt
ω=Δθ/Δt =2π/T= 2πf
x= Acos(2πft)
v=-Aωsin(2πft)
ω=√k/m
a=-Aω2cos(2πft)

9. Motion of a pendulum
Ft=-mg sinθ =-mg θ
Ft= mg sin(s/L)
Ft=-(mg/L)s
Ft=-kx
k= mg/L
ω=2πf= √k/m
ω=√mgL/m=√g/L
T= 2π√g/L

10. Simple harmonic motion for an object-spring system, and its analogy, the motion of a simple pendulum

11. Wave-the motion of a disturbance
Transverse waves- each segment of the rope that is disturbed moves in a direction perpendicular to the wave motion
Longitudinal waves- the elements of the medium undergo displacements parallel to the direction of wave motion (sound waves)

12. Frequency, Amplitude and wavelength:
v=Δx/Δt
Δx=λ; Δt=T
v= λ/T
v=f λ
The wavelength λ- is the distance between 2 successive points that behaves identically
The speed of waves on strings: v=√F/μ
(F-tension, μ- linear density-mas of the string/unit length

13. Interference of waves
Two traveling waves can meet and pass through each other without being destroyed or even altered
The superposition principle: when 2 or more traveling waves encounter other while moving through a medium, the resultant wave is found by adding togherther the displacements of the individual waves point by point (constructive interference or destructive interference)