Periodic Motion

1
Periodic Motion

• Recall that

• Using the fact that the maximum displacement is
  A, the work energy theorem states

2

• Solving for the velocity, get

• Using the solution for position, the velocity
  becomes

3
Graphical Interpretation
4
Importance of Periodic Motion

• All atomic and molecular bonds can be
  approximated by springs
• All signals can be decomposed into sets of
  periodic motions
• Non periodic motion can also be decomposed into
  sets of periodic motions

5
Simple Pendulum

• Newtons second law yields

6

• For small angles, sinq q
• Recall that q x/r, a a/r, so

• Comparing with Hookes Law, see that

7
Waves

• So far have only looked at periodic motion that
  is periodic in time.
• Can also have periodicity in space

8
Characteristics of Waves

• In addition to amplitude, period and frequency,
  also have wavelength.
• Wavelength is the distance covered by a cell of
  periodic motion
• Two classes of waves
• Mechanical waves
• Requires external source of energy
• Requires medium to travel through
• Electromagnetic waves
• Carries its own energy
• Does not need a medium

9
Types of waves

• Transverse
• Changes in amplitude are perpendicular to motion
  of wave
• Longitudinal
• Changes in amplitude are parallel to motion of
  wave
• Solitons
• Solitary wave fronts that propagate by themselves