13.1) Hooke's Law

  Fs=-kx
  
  Where k is the spring constant.
  
  Simple Harmonic Motion - the net force along the direction of motion is a
  Hooke's Law type of force.  That is, the net force is proportional to the
  displacement and opposite in the direction.
  
  
  Amplitude - A - is the maximum distance travelled from the equilibrium point.
  
  Period - T - the time is takes to execute one complete cycle of motion.
  
  frequency - f - number of cycles per unit of time.

  
  Since F=ma and Fs=-kx, it follows that ma=-kx.
  
  a=-km/x
  
  Where little a is the acceleration and k is the spring constant.

  
13.2) Elastic Potential Energy

  PEk ≡ 1/2 kx2  

  These can be combined with the other equations for potential and kinetic
  energy we learned from Ch. 5.
  
  (KE + PEg + PEs)i = (KE + PEg + PEs)f
  
13.3) Velocity as a function of position

  v = ± sqrt(k/m * (A2-x2))
  
  where k is the spring constant and A is the amplitude.
  

13.4) Comparing Simple Harmonic Motion with Uniform Circular Motion

  If we replace k/m with a constant C, then the preceding equation becomes:
  
  v = C sqrt(A2 - x2)
  
  which also models uniform circular motion
  
  [see picture on pp. 414]
  
  
  Period and Frequency
  
  T = 2 Π sqrt(m/k)
  
  where T is the period and Π is the constant pi.
  
  f = 1/T
  
  combining the two preceding equations:
  
  f = (1 / 2π) sqrt(k/m)
  
  The units of frequency are seconds-1, or hertz (Hz).
  
  ω = 2πf = sqrt(k/m)
  
  Where ω is the angular frequency.
  
  
13.5) Position, Velocity, and Acceleration as a function of Time

  x = A cos(ωt)   where t is time.
  
  ω = Δθ/Δt = 2π/T = 2πf
  
  
13.6) Motion of a Pendulum
  
  Ft=-mgsinθ
  
  Where Ft is the force due to tension in the pendulum.
  
  For small angles, less than 15 degress or so, the sinθ ≈ θ, 
  where θ is express in radians.
  
  Ft=-mgθ 
  
  T = 2πsqrt(L/g)
  
  where L is the length of the string in the pendulum.
  
13.7) Damped Oscillations

  underdamped oscillations - osciallates about the equilibrium point to some 
  degree before coming to rest.
  
  critically damped - the system does not oscillate, it starts at a certain 
  amplitude and comes to rest at the equilibrium point without passing through
  it
  
  overdamped - the system does not oscillate, it starts at a certain amplitude
  and moves slowly to the equilibrium point.  It is more than critically damped
  which is why it moves slower.
  
13.8) Wave motion

  wave - a disturbance in a fluid that moves from one point to another.  That is
  to say, the disturbance moves but the fluid is not carried with it, the fluid 
  simply oscillates.
  
13.9) Types of waves

  traveling wave - the wave moves in a direction and the medium oscillates
  perpendicular to that direction
  
  standing wave - the medium osciallates up and down across the entire medium, 
  giving the appearance that the wave is not moving
  
  longitudinal waves - the particles of the medium undergo motion parallel to
  the to the movement of the wave.  Sound waves are longitudinal.
  
13.10) Frequency, amplitude, and wavelength

  A = amplitide = maximum height of the wave
  
  λ = wavelength = length of a full cycle of a wave
  
  f = frequency = number of wavelengths that pass a particular points in a 
  second
  
  T = period = amount of time it takes for one wavlength to pass a particular
  point = 1/f;
  
  v = λ/T  
  
  v = fλ

13.11) the speed of strings
  
  F = tension in a string (a type of Force)
  
  μ = the mass per length of the string
  
13.12) Superposition and interference of waves

  Superposition principle - If two or more traveling waves are moving through a
  medium, the resultant wave is found by adding together the displacements of 
  the individual waves point by point.
  
  crest - high point of a wave at the amplitude
  
  trough - low point of a wave at the amplitude
  
  constructive inerference - a crest meets a creets creating a point with a 
  height that is the sum of the two amplitdues
  
  destructive interference - a crest meets a trough and they cancel each other 
  out to some degree
  
13.13) Reflection of waves

  Example:  A string is tied to an object.  A waves passes through the string,
  when it reaches the object it 'bounces' off of the object and moves in the 
  opposite direction.
  
  
HW 5:
p. 433 # 1; 
p. 434 Problem # 1
p. 435 # 5
p. 436 # 13
p. 437 # 27, 39
p. 438 # 44, 46