Chapter J  Problems
Blinn College  Physics 2425  Terry Honan
Problem J.1
The position as a function of time for a particle in simple harmonic motion is
x
H
t
L
=
H
4 cm
L
cos
AI
3
p
s

1
M
t
+p
E
.
(a) What are the period and frequency?
(b) What is the amplitude of the oscillation?
(c) What is the phase angle?
(d) What is the maximum speed and maximum acceleration?
(e) At
t
=
0.25 s what is the position of the particle?
(f) Suppose this describes the postion of a 0.6 kg mass at the end of a spring. What is the spring constant?
Solution to J.1
The general form for simple harmonic motion is
x
H
t
L
=
A
cos
H
w
t
+f
L
.
Here we have
x
H
t
L
=
H
4 cm
L
cos
AI
3
p
s

1
M
t
+p
M
ï
A
=
4 cm ,
w =
3
p
rad
s
and
f = p
(a)
T
=
2
p
w
=
2
3
s and
f
=
w
2
p
=
1.5 Hz
(b)
A
=
4 cm
(c)
v
max
= w
A
=
3
p
H
0.04
L
=
0, 377
m
ê
s
and
a
max
= w
2
A
=
H
3
p
L
2
0.04
=
3.55 m
ë
s
2
(d)
f = p
(e)
x
H
0.25
s
L
=
4 cos
H
3
p μ
0.25
+ p
L
=
2.83 cm
(Note that your calculator must be in the radians mode to evaluate the above expression.)
(f) For a mass/spring system:
w =
k
m
ï
k
=
m
w
2
=
53.3
N
ê
m
Problem J.2
When a mass is hung from a spring is stretches it by 15 cm. What is the period of the oscillations of this system?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Simple Harmonic Motion, Robert Hooke, H4 cmL cosAI3

Click to edit the document details