elam (lbe244) – HW13 – markert – (56475)
1
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21
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001
10.0 points
An ideal massless spring is fixed to the wall
at one end, as shown below. A block of mass
M
attached to the other end of the spring
oscillates with amplitude
A
on a frictionless,
horizontal surface.
The maximum speed of
the block is
v
m
.
m
k
0

A
+
A
v
m
What is the force constant
k
of the spring?
1.
k
=
m v
2
m
2
A
2.
k
=
m g
A
3.
k
=
m g v
m
2
A
4.
k
=
m v
2
m
2
A
2
5.
k
=
m v
2
m
A
2
correct
Explanation:
For the ideal harmonic oscillation of the
spring system, the kinetic energy maximum is
equal to the potential energy maximum which
is also the total energy of the system, so we
obtain
1
2
k A
2
=
1
2
m v
2
m
k
=
m v
2
m
A
2
.
002 (part 1 of 3) 10.0 points
A block of unknown mass is attached to a
spring of spring constant 7
.
9 N
/
m and under
goes simple harmonic motion with an ampli
tude of 4
.
8 cm.
When the mass is halfway
between its equilibrium position and the end
point, its speed is measured to be 29
.
2 cm
/
s.
Calculate the mass of the block.
Correct answer: 0
.
160105 kg.
Explanation:
Let :
k
= 7
.
9 N
/
m
,
A
= 4
.
8 cm
,
and
v
= 29
.
2 cm
/
s
.
If the maximum displacement (amplitude) is
A
, the halfway displacement is
A
2
. By energy
conservation,
K
i
+
U
i
=
F
f
+
U
f
0 +
1
2
k A
2
=
1
2
m v
2
+
1
2
k
A
2
2
k A
2
=
m v
2
+
1
4
k A
2
m
=
3
k A
2
4
v
2
=
3 (7
.
9 N
/
m) (0
.
048 m)
2
4 (0
.
292 m
/
s)
2
=
0
.
160105 kg
.
003 (part 2 of 3) 10.0 points
Find the period of the motion.
Correct answer: 0
.
894476 s.
Explanation:
ω
=
k
m
=
7
.
9 N
/
m
0
.
160105 kg
= 7
.
02443 rad
/
s
,
so the period is
T
=
2
π
ω
=
2
π
7
.
02443 rad
/
s
=
0
.
894476 s
.
004 (part 3 of 3) 10.0 points
Calculate the maximum acceleration of the
block.
Correct answer: 2
.
36844 m
/
s
2
.
Explanation:
Simple harmonic motion is described by
x
=
A
cos
ω
t ,
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elam (lbe244) – HW13 – markert – (56475)
2
so the acceleration is
a
=

ω
2
A
cos
ω
t .
The maximum of the cosine function is 1, so
the maximum acceleration is
a
max
=
ω
2
A
= (7
.
02443 rad
/
s)
2
(0
.
048 m)
=
2
.
36844 m
/
s
2
.
This happens when the block is at its turning
point (maximum displacement).
005
10.0 points
The displacement in simple harmonic motion
is maximum when the
1.
velocity is zero.
correct
2.
acceleration is zero.
3.
linear momentum is a maximum.
4.
velocity is a maximum.
5.
kinetic energy is a maximum.
Explanation:
The maximum displacement occurs at the
turning points, which are the points where the
velocity is zero.
006
10.0 points
When an object oscillating in simple harmonic
motion is at its maximum displacement from
the equilibrium position, which of the follow
ing is true of the values of its speed and the
magnitude of the restoring force?
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 Spring '08
 ERSKINE/TSOI
 Energy, Decibel, Correct Answer, Elam

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