Notes
• Reminder: First Exam Friday, 1:55-3:50pm, Jordan
H ll lab
Hall
l b room
– Will cover Gravity, Fluids (Ch.13, 14)
– Review Session: Tomorrow, 7:30-9:30pm, NSH 118
• Office Hours:
– By appointment the rest of the week
• Colloquium Today:
– “The 2011 Nobel Prize: A personal view”
SHM and Rotation

A mass attached to a spring oscillates back and forth as
indicated in the position vs. time plot below. At point P,
the mass has
1. positive velocity and positive acceleration.
2. positive velocity and negative acceleration.
3 positive velocity and zero acceleration.
3.
acceleration
4. negative velocity and positive acceleration.
g
velocityy and negative
g
acceleration.
5. negative
6. negative velocity and zero acceleration.
7. zero velocity but is accelerating (positively or negatively).
8. zero velocity and zero acceleration.
A mass suspended from a spring is oscillating up and
down. Consider two possibilities:
(i) at some point during the oscillation the mass has zero
velocity but is accelerating (positively or negatively);
(ii) at some point during the oscillation the mass has
zero velocity and zero acceleration.
1. Both occur sometime during the oscillation.
2. Neither occurs during the oscillation.
3 Only
3.
O l (i) occurs.
4. Only (ii) occurs.
Energy in SHM
E
U( ) = ½ kx2
U(x)
Etot
KE(x
( 1) = ½ mv2
U(x1) = ½ kx12
x1
x
A mass is attached to a spring of spring constant 8 N/m.
The angular frequency  of its motion is 2 rad/s, the
amplitude of its motion is 1 m. At time t = 0, the phase
of the oscillatory motion is +53° away from zero.
Find:
a) the position of the mass at t = 0
b) the velocity of the mass at t = 0
c) the total energy of the system
d) the maximum velocity
e) the mass
f) the time at which the maximum kinetic energy is first
reached.
A simple harmonic oscillator consists of a block of mass
m = 2.00 kg attached to a spring of constant k = 100
N/m. When t=1.00 sec, the position and velocity of the
block are x = 0.129 meters and v = 3.415 m/s,
respectively.
a) What is the amplitude of the oscillations?
What
W
a were
we e thee (b) position
pos o and
a d (c) velocity
ve oc y at
a timee tt=0?
0?
Oscillating Systems
Ultimate bungee jumping: a straight tunnel is dug all of
the way through the earth. You are dropped into the
frictionless tube that lines the tunnel and appear on the
other side, only to fall back into the hole. Show that
your motion is simple harmonic motion, and find the
period.
A pendulum is made of a rod of length L=1 m and mass mrod =3
k attached
kg,
tt h d to
t a solid
lid sphere
h off radius
di R=0.2
R 0 2 m and
d mass msphere
= 4.5 kg. The axis of rotation is at the end of the rod.
a)) Wh
Whatt is
i the
th momentt off inertia
i ti off
the system about the rotation axis?
b) Where is the center
center-of-mass
of mass of the
pendulum relative to the axis of
rotation?
c) Write down Newton’s 2nd Law (for
rotational motion) for the system
configuration shown. Assume the
angular displacement  is small.
d) Find the period of the pendulum for
small angular displacement .
pivot

L = 1m
R = 0.2 m