PH101 HW Waves - This print-out should have 23 questions...

This print-out should have 23 questions.
Multiple-choice questions may continue on
the next column or page – find all choices
before answering.
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 non-calculus 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.

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.