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001
10.0 points
A particle oscillates up and down in simple
harmonic motion. Its height
y
as a function
of time
t
is shown in the diagram.
1
2
3
4
5
5
5
y
(cm)
t
(s)
At what time
t
in the period shown does
the particle achieve its maximum positive ac
celeration?
1.
None of these; the acceleration is con
stant.
2.
t
= 3 s
3.
t
= 1 s
correct
4.
t
= 4 s
5.
t
= 2 s
Explanation:
This oscillation is described by
y
(
t
) =

sin
π
t
2
,
v
(
t
) =
d y
dt
=

π
2
cos
π
t
2
a
(
t
) =
d
2
y
dt
2
=
π
2
2
sin
π
t
2
.
The maximum acceleration will occur when
sin
π
t
2
= 1, or at
t
= 1 s
.
From a noncalculus perspective, the veloc
ity is negative just before
t
= 1 s since the
particle is slowing down. At
t
= 1 s, the par
ticle is momentarily at rest and
v
= 0. Just
after
t
= 1 s , the velocity is positive since
the particle is speeding up.
Remember that
a
=
Δ
v
Δ
t
,
acceleration is a positive maximum
because the velocity is changing from a nega
tive to a positive value.
002
10.0 points
A 128 N object vibrates with a period of 4.76
s when hanging from a spring.
What is the spring constant of the spring?
The acceleration of gravity is 9
.
81 m
/
s
2
.
Correct answer: 22
.
7346 N
/
m.
Explanation:
Let :
F
g
= 128 N
,
T
= 4
.
76 s
,
and
g
= 9
.
81 m
/
s
2
.
T
= 2
π
m
k
T
2
π
2
=
m
k
k
=
m
2
π
T
2
=
F
g
g
2
π
T
2
=
128 N
9
.
81 m
/
s
2
2
π
4
.
76 s
2
=
22
.
7346 N
/
m
.
003
10.0 points
A 52
.
2 g object is attached to a horizontal
spring with a spring constant of 14
.
8 N
/
m
and released from rest with an amplitude of
25
.
1 cm.
What is the velocity of the object when it
is halfway to the equilibrium position if the
surface is frictionless?
Correct answer: 3
.
66016 m
/
s.
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Explanation:
Let :
m
= 52
.
2 g = 0
.
0522 kg
,
k
= 14
.
8 N
/
m
,
and
A
= 25
.
1 cm = 0
.
251 m
.
The speed is
v
=
k
m
(
A
2

x
2
)
=
14
.
8 N
/
m
0
.
0522 kg
[(0
.
251 m)
2

(0
.
1255 m)
2
]
=
3
.
66016 m
/
s
.
004
(part 1 of 3) 10.0 points
A 541 g mass is connected to a light spring
of force constant 3 N
/
m that is free to oscillate
on a horizontal, frictionless track. The mass
is displaced 6 cm from the equilibrium point
and released from rest.
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 Spring '08
 Jones,S
 Physics, Simple Harmonic Motion, Frequency, Wavelength, Correct Answer

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