Announcements

1
Announcements

• New homework
• (Ch. 13, Problems 11, 14 28)
• Office hours
• M 1-2 pm
• TWF 3-4 pm
• R 10-11 am
• Tutorial Learning Center - Houston Hall 120/110
• M 8-10 am, 11-noon, 1-7 pm R 9-1 pm, 2-7 pm,
  7-9 pm
• T 9-noon, 1-7 pm, 7-9 pm F 8-1 pm, 2-5 pm
• W 8-9 am, 11-noon, 2-7 pm, 7-9 pm (Grand
  Mesa Hall)

2
Chapter 13

• Vibrations Waves
• (Simple Harmonic Motion)

3
Last time

• Hookes Law
• Elastic Potential Energy
• Acceleration of SHO
• Amplitude, Frequency, Period

4
Energy in S.H.M.
KE max
x 0
x -A
x A
PE max
5
Velocity as a function of position
Suppose an object is initially at its maximum
extension A. What is the velocity of the object
for an arbitrary position x?
A
x
x 0
Using Conservation of Energy
6
Question 1

• A mass m, oscillating on the end of a spring with
  spring constant k has an amplitude A. Its
  maximum speed is

7
Question 2

• A (frozen) turkey attached to a spring undergoes
  simple harmonic motion on a horizontal
  frictionless surface. Its total energy is 50 J.
  
• When the displacement is half the amplitude, the
  kinetic energy is
• 0
• 12.5 J
• 25 J
• 37.5 J
• 50 J

8
Simple Harmonic Motion

Newtons Second Law
x
Fs
m
x 0
The box undergoes simple harmonic motion
described by
9
Oscillation Terminology

• Period
• T of seconds/cycle
  T s
• Frequency
• f of cycles/second
  f 1/s Hz
• Angular Frequency
• ? of radians/second
  ? rad/s

10
Quiz Question 1

• An object of mass m is attached to a horizontal
  spring, stretched to a displacement A from
  equilibrium and released, undergoing harmonic
  oscillations on a frictionless surface with
  period T0. The experiment is then repeated with
  a mass of 4m.
• What is the new period of oscillation?
• 2 T0
• T0
• T0 /2
• T0 /4

11
Quiz Question 2

• Consider the situation in Quiz Question 1. The
  subsequent total mechanical energy of the object
  with mass 4m is
• greater than
• less than
• equal to
• the original total mechanical energy.

12
Velocity Acceleration

• If the displacement (as a function of time) of
  the oscillator is given by
• what is velocity acceleration as a function of
  time?

13
Section 13.4 Position, Velocity Acceleration
as a Function of Time

• Displacement
• Velocity
• Acceleration

14
i.e. Fisher Price Kiddie Ride

• Is this ride safe?

A 1m T 1s
2 m
15
Quiz Question 3

• If the amplitude of a system in simple harmonic
  motion is doubled, which of the following
  quantities doesnt change?
• Total energy
• Maximum speed
• Maximum acceleration
• Period

16
Section 13.5
Motion of a Pendulum

• What is the period of a simple pendulum?
• Notice
• valid for small ?
• Period, T, is independent of the mass!
• Know T, get L

?
L
m
17
S.H.M. for an Object-Spring System a Simple
Pendulum