Important Reminders
 Last Lecture
Simple Harmonic Motion - Summary
Intro to Simple Harmonic Motion
 IAP class schedule posted under “General Info”
 Today
More on Simple Harmonic Motion
 Lecture M 11-12, T 10-12, W 10-12, F 11-12
Intro to more accurate gravity formula
 Some recitations moved, all still on Thursday.
The physics of the motion is in the mass and spring
constant which determine the period of each oscillation.
The amplitude does not affect the period.
 Pset #9 due next Friday.
ax = "A! 2 cos(! t)
 Have a relaxing holiday!
t=0 when speed is maximum
"
and therefore a=0
!=
and therefore x=0
2
Gravity depends on M and inverse of distance squared.
8.01L Fall 2005
11/22/2005
Energy in SHM
11/22/2005
 Assume you know x & v at t=0. Call them: x0 v0
1
1
ETotal = KE + PE = mv 2 + kx 2
2
2
2
m ( A! )
kA 2
2
=
( cos(! t + " )) +
(sin(! t + " ))2
2
2
kA 2 1 2
ETotal =
= mvMax
2
2
2
kA
1 2 1 2 1 2
= mv + kx = mvMax
2
2
2
2
8.01L Fall 2005
8.01L Fall 2005
11/22/2005
 Then: x0 = A cos(! ) v0 = "A# sin(! )
x = Asin(! t)
vx = A! cos(! t)
ax = "A! 2 sin(! t)
8.01L Fall 2005
Simple Harmonic Motion - General
 Summary:
11/22/2005
Gravity far from the Surface
 Force depends on:
the product of the two masses
the inverse square of the distance
"v0
 Solve: tan(! ) =
# x0
v2
A = x + 02
!
a universal constant:
2
0
 For small amplitudes, a pendulum will also oscillate
with simple harmonic motions with frequency:
11/22/2005
G = 6.673 ! 10 "11
Nm 2
kg 2
 Force points along the line between the two objects
in the direction to cause attraction
FG = !
! = gL
8.01L Fall 2005
! = km
t=0 when position is maximum x = A cos(! t)
and therefore v=0 ! = 0
vx = "A! sin(! t)
Give someone else an opportunity to be thankful.
Give blood at the student center today until 8pm.
Energy oscillates between Kinetic and Potential.
dt 2
 General solution: x = A cos(! t + " )
 Practical solutions:
 MasteringPhysics due next Tuesday
 Important Concepts
2
 Basics: Fx = !kx = m d x
8.01L Fall 2005
GM 1 M 2
r̂
r2
11/22/2005
1