Periodic Motion

Front 1

Wave Properties

Back 1

• Amplitude
  
• Wavelength
• Frequency
• Wave Speed
• Resonance

Front 2

Simple Harmonic Motion

Back 2

An object oscillates back and forth from an equilibrium point with an angular frequency (w) and is subject to linear restoring force.

• Always directed back towards equilibrium.
• Magnitude ~ Displacement from the Equilibrium position.

Front 3

Frequency

Back 3

f= 1 / time
SI units: 1/ sec or Herz (Hz)

Front 4

Angular Frequency

Back 4

Is the change in angle per time described by the particles path as it moves around the circle.

• w= 2(pi)f= 2pi/ time

Front 5

Pendulums

Back 5

Simple Harmonic Moti

Front 6

Uniform Circular Motion (Rev)

Back 6

1 Rev/ sec= Particles moving at circular path at constant speed.

Front 7

Springs

Back 7

w (angular frequency)= square-root (k/ m)

w= sqr(k/ m)

Front 8

Hooke's Law

Back 8

F= -kx

• d=x (extended spring)
• d=0 (spring at equilibrium)
• d=(neg)x (coiled spring).

Front 9

Newtons 2nd Law

Back 9

F=-(k)(x)

a=-(w^2)(x)

Front 10

Spring Constant (k)

Back 10

Stiffness

• Strong Spring > k > Less resistant
  

Front 11

Spring and Pendulum

Back 11

k= mg/ L

Pendulum= sq (g/L)

Front 12

Hooke Law

Back 12

When mass = equilibrium

• KE= 1/2m(v^2) and PE=0

When Oscillation= Xmas (displacement)

• PE=Umax= 1/2K(A^2) and KE=0
  
  

Front 13

Point of Max Acceleration in Hooke-Law

Back 13

Acceleration is proportional to distance (x), the acceleration will be greatest when displacement from equilibrium is maximized.
F=-kx
F=ma
And so ma=-kx

Front 14

KNOW This- Spring Constant and Frequency

Back 14

w= sq(k/ m)= 2(pi(f)

Front 15

Potential Energy for Spring and Pendulum

Back 15

Mass Spring=1/k(x^2)

Simple Pendulum= mgh

Front 16

Kinetic Energy for Spring and Pendulum

Back 16

Both are 1/m(v^2)

Front 17

Angular Frequency (w) for Spring and Penduclum

Back 17

Spring= sqr (k/ m) = 2pi(f)

Pendulum= sqr (g/ L) = 2pi(f)

BOTH EQUAL to 2pi(f)