Solution of HW3 – Phys 310 00 Intermediate Mechanics Fall 2011
SHO – Simple Harmonic Oscillations
Problem #1 15 points
a.
According to picture.
period: 4
ʌ
spring constant:
2
2
2
2
2
1
1
2
0.5
*
4
8
8
m
N
T
k
m
kg
s
m
k
T
S
S
S
S
§
·
§
·
¨
¸
¨
¸
©
¹
©
¹
2
1
1
*
8
8
N
k
kg
s
m
b.
0
1
( )
cos(
)
4
2
2
1
4
2
0.4
x t
A
t
T
s
T
A
m
Z
I
S
S
S
Z
S
±
²
0
( )
( )
sin(
)
dx
v t
x t
A
t
dt
Z
Z
I
±
²
±
To determine
0
I
we need to use initial conditions. According to picture x(0)=0 at equilibrium
position
0
0
0
(0)
cos(
*0
)
0
*0
2
2
x
A
S
S
Z
I
Z
I
I
²
²
Then
1
( )
0.4cos(
)
2
2
1
( )
0.2sin(
)
2
2
x t
t
v t
t
S
S
²
±
²
c.
Disagree. This formula
0
S
v
t
works only in case of constant velocity. In case of oscillations
0
v
is not constant.
Energy conservation law helps us to determine
0
v
:
2
2
2
2
0
0
0
0.125
0.4
0.2
2
2
0.5
v
kA
kA
k
m
m
v
v
A
s
m
m
0
0.2
m
v
s

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