This preview shows pages 1–2. Sign up to view the full content.
Phys. 315, Spring 2012
Homework #1
Due: Weds., Jan 25, start of class.
1. (10 points) French, problem 11. Do this problem by working with the real and
imaginary parts
a, b, c,
and
d
of
12
and
.
zz
You may find the following trigonometric sum
relation helpful:
± ²
± ² ± ²
± ² ± ²
tan
tan
tan
1t
a
n
t
a
n
DE
³
³
´
(CRC Standard Mathematical Tables,
31
st
edition, section 6.1.11 )
2. (6 points) Find the magnitude
A
and the phase angle
I
of the vectors
1
23
,
zi
³
and
± ²
2
2
´
in the complex plane.
3. (8 points) French, problem 18.
4. (14 points) Simple Harmonic Oscillator equation
.
The equation that describes the oscillation of a mass
m
suspended by a spring of spring
constant
k
is
2
2
0,
d
mk
dt
[
where
is the displacement of the mass from its
equilibrium position.
a) Verify that
± ²
( )
cos
tA
t
[Z
³
is a solution of this equation if and only if
k
m
Z
.
b) Suppose that you know that
± ²
( )
cos
t
³
for some definite values of
A
and
.
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 '08
 Staff
 Work

Click to edit the document details