HOMEWORK QUESTION

1
HOMEWORK QUESTION

• Please do this question and hand it by Tuesday
  after the reading week, in class
• A 50kg child slides down a 45o frictionless hill
  for 60m, starting with an initial velocity of
  2m/s. The child then slides for 10m over a flat
  surface that has a coefficient of kinetic
  friction of 0.15, and finally back up another
  frictionless hill with a slope of 30o.
• Draw a pictures of the problem and determine how
  far on the 2nd hill the child ends up (not the
  height).

2
Oscillatory Motion (Chapter 14)

• Kinematics of Simple Harmonic Motion
• Mass on a spring
• Energy

Knight sections 14.1-14.6
3
Oscillatory Motion
We have examined the kinematics of linear motion
with uniform acceleration. There are other
simple types of motion. Many phenomena are
repetitive or oscillatory. Example Block and
spring, pendulum, vibrations (musical
instruments, molecules)
4
Spring and mass
Equilibrium no net force
5
SHM
x(t)
T
A
A amplitude f phase constant w angular
frequency
t
-A
A is the maximum value of x (x ranges from A to
-A). f gives the initial position at t0
x(0) A cosf . w is related to the period T and
the frequency f 1/T T (period) is the time for
one complete cycle (seconds). Frequency f (cycles
per second or hertz, Hz) is the number of
complete cycles per unit time.
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In general
Three constants specify the motion Amplitude,
A Angular Frequency, w Initial phase (or phase
constant), f
These graphs are a mathematical representation of
motion as a functionof time, now how the object
actually moves notice the axes. x(t) is
simply the displacement from some position.
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The quantity (w t f) is called the phase, and
is measured in radians. The cosine function
traces out one complete cycle when the phase
changes by 2p radians. The phase is not a
physical angle!
The period T of the motion is the time needed to
repeat the cycle

units radians/second or s-1
8
Example
The block is at its equilibrium position and is
set in motion by hitting it (and giving it an
initial velocity) at time t 0. Its motion is
SHM with amplitude 5 cm and period 2 seconds.
Write the function x(t).
M
v0
x
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QUIZ
The block is at x0 5 cm, with positive
velocity v0, at time t 0. Its motion is SHM
with amplitude 10 cm and period 2 seconds. If
x(t) A cos (wt f), the phase constant f
should be
M
v0
x0

1. 0o
2. 30o
3. 60o
4. -30o
5. -60o