Le (tl8426) – HW11 – gentle – (56245)
1
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printout
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have
8
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before answering.
001
10.0points
A simple harmonic oscillator has amplitude
0
.
56 m and period 2
.
9 sec.
What is the maximum acceleration?
1.
0
.
0665874 m
/
s
2
2.
7
.
62342 m
/
s
2
3.
0
.
418381 m
/
s
2
4.
2
.
62877 m
/
s
2
correct
5.
1
.
31438 m
/
s
2
6.
0
.
193103 m
/
s
2
Explanation:
Let :
A
= 0
.
56 m
and
T
= 2
.
9 sec
.
For a simple harmonic oscillator, the dis
placement is
x
=
A
cos
parenleftbigg
2
π
T
t
+
φ
parenrightbigg
,
so the acceleration is
a
=
d
2
x
dt
2
=

A
parenleftbigg
2
π
T
parenrightbigg
2
cos
parenleftbigg
2
π
T
t
+
φ
parenrightbigg
.
Since

1
<
cos
α <
1, the maximum acceler
ation is
A
max
=
4
π
2
A
T
2
=
4
π
2
(0
.
56 m)
(2
.
9 sec)
2
=
2
.
62877 m
/
s
2
.
002
10.0points
Simple harmonic motion can be described us
ing the equation
x
=
x
m
sin(
ωt
+
φ
)
.
If
x
0
= initial position,
v
0
= initial velocity,
then
1.
tan
φ
=

ω x
0
v
0
2.
tan
φ
=

v
0
ω x
0
3.
tan
φ
= +
v
0
ω x
0
4.
tan
φ
= +
ω x
0
v
0
correct
Explanation:
x
=
x
m
sin(
ω t
+
φ
)
v
=
d x
dt
=
x
m
ω
cos(
ω t
+
φ
)
When
t
= 0,
x
0
=
x
m
sin
φ
v
0
=
x
m
ω
cos
φ
x
m
sin
φ
x
m
ω
cos
φ
=
x
0
v
0
tan
φ
=
ω x
0
v
0
.
003
10.0points
A 54 kg person steps into a car of mass
2761 kg, causing it to sink 0
.
59 cm on its
springs.
Assuming
no
damping,
with
what
fre
quency will the car and passenger vibrate on
the springs?
The acceleration of gravity is
9
.
81 m
/
s
2
.
Correct answer: 0
.
898848 Hz.
Explanation:
Let :
m
= 54 kg
,
M
= 2761 kg
,
g
= 9
.
81 m
/
s
2
,
and
Δ
x
= 0
.
59 cm = 0
.
0059 m
.
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Le (tl8426) – HW11 – gentle – (56245)
2
The spring force is
F
=
k
Δ
x
k
=
F
Δ
x
=
m g
Δ
x
,
where
m
is the person’s mass.
The frequency is
f
=
1
2
π
radicalbigg
k
m
+
M
=
1
2
π
radicalbigg
m g
(
m
+
M
) Δ
x
=
1
2
π
radicalBigg
(54 kg) (9
.
81 m
/
s
2
)
(54 kg + 2761 kg) (0
.
0059 m)
=
0
.
898848 Hz
.
004
10.0points
A horizontal platform vibrates with simple
harmonic motion in the horizontal direction
with a period of 2
.
81 s. A body on the plat
form starts to slide when the amplitude of
vibration reaches 0
.
438 m.
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 Fall '07
 Swinney
 mechanics, Force, Friction, Mass, Simple Harmonic Motion, Amax ω

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