Physics 321 – Spring 2006
Homework #6, Due at beginning of class Wednesday Mar 1.
1. [4 pts] A hook is at height
y
above the floor, where
y
is constant for all negative
times:
y
=
y
0
for
t <
0. For positive times,
y
oscillates:
y
=
y
0
+
A
sin
ωt
for
t >
0. A mass
M
hangs from an ideal spring attached to this hook. The mass is
at height
x
above the floor. The mass hangs motionless at
x
=
x
0
=
y
0

Mg/k
for
t <
0, where
k
is the spring constant. Let
ω
0
=
q
k/M
as usual.
(a) Find the motion
x
(
t
) of the mass for
t >
0 if
ω
= 2
ω
0
.
(b) Find the motion
x
(
t
) of the mass for
t >
0 if
ω
=
ω
0
. (You can do this by
first finding
x
(
t
) for arbitrary
ω
and then carefully taking the limit
ω
→
ω
0
; or
if you’re chicken, you can set
ω
→
ω
0
in the equation of motion and solve it.)
2. [4 pts] A driven harmonic oscillator obeys the equation
¨
x
+
x
=
t
(
A

t
) for 0
< t < A
. Given the initial conditions
x
= ˙
x
= 0 at
t
= 0,
find the subsequent motion
x
(
t
) during the time interval 0
< t < A
.
3. [4 pts] Marion & Thornton, problem 320 (Same in 4th edition). Do this problem
by hand (i.e., using algebra, not using a computer). You need to find the two
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 Spring '08
 B.Pope
 mechanics, Kinetic Energy, Mass, Work, pts, class Wednesday Mar

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