Oscillatory%20Motion

1
Oscillatory Motion
2
Definitions

• Amplitude, A - Maximum displacement from
  equilibrium.
• Period, T - Time for one full oscillation.
• Frequency, f - Number of oscillations per unit of
  time.

Units (s-1 or Hz)
3
Harmonic Oscillator

• Restoring force is proportional to displacement.

Equilibrium
(1)
(2)
(3)
t 0s
(4) Try
(5)
X
A
-A
0
4
Angular Frequency

• In , w is angular
  frequency.
• In one time period, 2p wT.
• Units for w is rad/s.

5
Spring Constant

• A 500 g mass is attached to a spring and it
  oscillates 10 times in 15 seconds. What is the
  spring constant of the mass?
• How would this change on the moon?

6
Kinematics

• Displacement
• Velocity
• Acceleration

7
Jack-in-a-Box

• While initially at rest, a Jack-in-a-Box head is
  struck by a child's hand. The impulse of the
  strike gives the head an initial velocity of 0.3
  m/s. What is the maximum displacement of the
  head from equilibrium?
• (The mass of the head is 0.10 kg and the spring
  constant has a value of 1.5 N/m.)

8
Mass on a Spring

• At equilibrium,

9
Physical Pendulum

• Restoring force

10
Simple Pendulum

• All mass is concentrated at one point

l
q
mg

• Solution

11
Energy in a Spring

• Potential Energy
• Kinetic Energy
• Total Energy

12
Damped Oscillators

• Damping Force
• Newtons 2nd Law
• Solution to D.E.

13
Forced Oscillations

• Oscillating system has a natural frequency of w0
• Driving force is w
• The closer w0 and w are, the larger the amplitude

14
Resonance

• Maximum energy transfer between two objects that
  have similar oscillatory frequencies.

Tacoma Narrows Bridge
15
Phase Angle

• Phase, f , shifts the location of the peak
  displacement.
• f gt0 (shift to the left)
• f lt0 (shift to the right)

f
A
Amplitude
0
-A
0
T
2T
time
16
Torsion Pendulum

• Restoring force

17
Meter Stick Oscillations

• A meter stick has a length of 1 meter, a
  thickness of 8 mm and a width of 2.5 cm. The
  mass of the meter stick is 165 g.
• How many different ways can the meter stick be
  set up to oscillate and what is the angular
  frequency in each of these situations?