Download Chapter 15—Oscillatory Motion MULTIPLE CHOICE 1. A body of

Chapter 15—Oscillatory Motion
MULTIPLE CHOICE
1. A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached. It is
then displaced downward an additional 5.0 cm and released. Its position as a function of time is
approximately
a. y = 0.10 sin 9.9t
b. y = 0.10 cos 9.9t
c. y = 0.10 cos (9.9t + .1)
d. y = 0.10 sin (9.9t + 5)
e. y = 0.05 cos 9.9t
ANS: E
PTS: 2
DIF: Average
2. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time
according to the equation x = 5.0 cos (t). The magnitude of the acceleration (in m/s2) of the body at t
= 1.0 s is approximately
a. 3.5
b. 49
c. 14
d. 43
e. 4.3
ANS: B
PTS: 2
DIF: Average
3. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time
according to the equation x = 5 sin (t + /3). The phase (in rad) of the motion at t = 2 s is
a. 7/3
b. /3
c. 
d. 5/3
e. 2
ANS: A
PTS: 2
DIF: Average
4. A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time
according to the equation x = 5.0 sin (t + /3). The velocity (in m/s) of the body at t = 1.0 s is
a. +7.9
b. 7.9
c. 14
d. +14
e. 5.0
ANS: B
PTS: 2
DIF: Average
5. The motion of a particle connected to a spring is described by x = 10 sin (t). At what time (in s) is the
potential energy equal to the kinetic energy?
a. 0
b. 0.25
c. 0.50
d. 0.79
e. 1.0
ANS: B
PTS: 3
DIF: Challenging
6. The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then
be
a. 4 times as large
b. 3 times as large
c. 2 times as large
d. the same as it was
e. half as much
ANS: A
PTS: 1
DIF: Easy
7. A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure. The
mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is
approximately
a.
b.
c.
d.
e.
12
0.50
0.010
1.9
0.080
ANS: D
PTS: 2
DIF: Average
8. The mass in the figure slides on a frictionless surface. If m = 2 kg, k1 = 800 N/m and k2 = 500 N/m, the
frequency of oscillation (in Hz) is approximately
a.
b.
c.
d.
e.
6
2
4
8
10
ANS: C
PTS: 2
DIF: Average
9. Two circus clowns (each having a mass of 50 kg) swing on two flying trapezes (negligible mass,
length 25 m) shown in the figure. At the peak of the swing, one grabs the other, and the two swing
back to one platform. The time for the forward and return motion is
a.
b.
c.
d.
e.
10 s
50 s
15 s
20 s
25 s
ANS: A
PTS: 2
DIF: Average
10. A uniform rod (mass m = 1.0 kg and length L = 2.0 m) pivoted at one end oscillates in a vertical plane
as shown below. The period of oscillation (in s) is approximately
a.
b.
c.
d.
e.
4.0
1.6
3.2
2.3
2.0
ANS: D
PTS: 2
DIF: Average
11. A horizontal plank (m = 2.0 kg, L = 1.0 m) is pivoted at one end. A spring (k = 1.0  103 N/m) is
attached at the other end, as shown in the figure. Find the angular frequency (in rad/s) for small
oscillations.
a. 39
b.
c.
d.
e.
44
55
66
25
ANS: A
PTS: 3
DIF: Challenging
12. The figure shows a uniform rod (length L = 1.0 m, mass = 2.0 kg) suspended from a pivot a distance d
= 0.25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is
approximately
a.
b.
c.
d.
e.
1.0
2.5
1.5
4.1
3.5
ANS: D
PTS: 3
DIF: Challenging
13. In the figure below, a disk (radius R = 1.0 m, mass = 2.0 kg) is suspended from a pivot a distance d =
0.25 m above its center of mass. For a circular disk,
. The angular frequency (in rad/s) for
small oscillations is approximately
a.
b.
c.
d.
e.
4.2
2.1
1.5
1.0
3.8
ANS: B
PTS: 3
DIF: Challenging
14. In the figure below, a hoop (radius R = 1.0 m, mass = 2.0 kg) having four spokes of negligible mass is
suspended from a pivot a distance d = .25 m above its center of mass. The angular frequency (in rad/s)
for small oscillations is approximately
a.
b.
c.
d.
e.
4.0
2.5
1.5
1.0
0.5
ANS: C
PTS: 3
DIF: Challenging
15. A torsional pendulum consists of a solid disk (mass = 2.0 kg, radius = 1.0 m) suspended by a wire
attached to a rigid support. The body oscillates about the support wire. If the torsion constant is 16
Nm/rad. What is the angular frequency (in rad/s)?
a.
b.
c.
d.
e.
2
4
6
8
7
ANS: B
PTS: 2
DIF: Average
16. The mass in the figure below slides on a frictionless surface. When the mass is pulled out, spring 1 is
stretched a distance x1 from its equilibrium position and spring 2 is stretched a distance x2. The spring
constants are k1 and k2 respectively. The force pulling back on the mass is:
a. k2x1.
b. k2x2.
c. (k1x1 + k2x2).
d.
.
e.
.
ANS: B
PTS: 2
DIF: Average
17. A hoop, a solid cylinder, and a solid sphere all have the same mass m and the same radius R. Each is
mounted to oscillate about an axis a distance 0.5 R from the center. The axis is perpendicular to the
circular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below.
Which is the correct ranking in order of increasing angular frequency ?
a.
b.
c.
d.
e.
hoop, cylinder, sphere
cylinder, sphere, hoop
sphere, cylinder, hoop
hoop, sphere, cylinder
sphere, hoop, cylinder
ANS: A
PTS: 2
DIF: Average
18. Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles
1, 2 and 3 respectively and released. The approximation sin  =  holds for all three angles, with 3
> 2 > 1. How do the angular frequencies of the three pendulums compare?
a. 3 > 2 > 1
b. Need to know amplitudes to answer this question.
c. Need to know
to answer this question.
d. 1 > 2 > 3
e. 1 = 2 = 3
ANS: E
PTS: 1
DIF: Easy
19. A weight of mass m is at rest at O when suspended from a spring, as shown. When it is pulled down
and released, it oscillates between positions A and B. Which statement about the system consisting of
the spring and the mass is correct?
a.
b.
c.
d.
e.
The gravitational potential energy of the system is greatest at A.
The elastic potential energy of the system is greatest at O.
The rate of change of momentum has its greatest magnitude at A and B.
The rate of change of gravitational potential energy is smallest at O.
The rate of change of gravitational potential energy has its greatest magnitude at A and B.
ANS: C
PTS: 1
DIF: Easy
20. An object of mass m is attached to string of length L. When it is released from point A, the object
oscillates between points A and B. Which statement about the system consisting of the pendulum and
the Earth is correct?
a.
b.
c.
d.
e.
The gravitational potential energy of the system is greatest at A and B.
The kinetic energy of mass m is greatest at point O.
The greatest rate of change of momentum occurs at A and B.
All of the above are correct.
Only (a) and (b) above are correct.
ANS: D
PTS: 1
DIF: Easy
Exhibit 15-1
A graph of position versus time for an object oscillating at the free end of a horizontal spring is shown
below. A point or points at which the object has positive velocity and zero acceleration is(are)
Use this exhibit to answer the following question(s).
21. Refer to Exhibit 15-1. A point or points at which the object has positive velocity and zero acceleration
is(are)
a. B
b. C
c. D
d. B and D
e. A and E
ANS: E
PTS: 1
DIF: Easy
22. Refer to Exhibit 15-1. The point at which the object has negative velocity and zero acceleration is
a. A
b. B
c. C
d. D
e. E
ANS: C
PTS: 1
DIF: Easy
23. Refer to Exhibit 15-1. The point at which the object has zero velocity and positive acceleration is
a. A
b. B
c. C
d. D
e. E
ANS: D
PTS: 1
DIF: Easy
24. Refer to Exhibit 15-1. The point at which the object has zero velocity and negative acceleration is
a. A
b. B
c. C
d. D
e. E
ANS: B
PTS: 1
DIF: Easy
25. In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a
horizontal plane under the action of a set of springs. If a 1.00 kg body vibrates at 1.00 Hz, a 2.00 kg
body will vibrate at
a. 0.500 Hz.
b. 0.707 Hz.
c. 1.00 Hz.
d. 1.41 Hz.
e. 2.00 Hz.
ANS: B
PTS: 2
26. At sea level, at a latitude where
DIF: Average
, a pendulum that takes 2.00 s for a complete swing back
and forth has a length of 0.993 m. What is the value of g in m/s2 at a location where the length of such
a pendulum is 0.970 m?
a. 0.098 3
b. 3.05
c. 9.57
d. 10.0
e. 38.3
ANS: C
PTS: 2
DIF: Average
27. Suppose it were possible to drill a frictionless cylindrical channel along a diameter of the Earth from
one side of the Earth to another. A body dropped into such a channel will only feel the gravitational
pull of mass within a sphere of radius equal to the distance of the mass from the center of the Earth.
The density of the Earth is 5.52  103 kg/m3 and G = 6.67  1011 Nm2/kg2. The mass will oscillate
with a period of
a. 84.4 min.
b. 169 min.
c. 24.0 h.
d. 1 130 h.
e. 27.2 d.
ANS: A
PTS: 2
DIF: Average
28. A 2.00 m-long 6.00 kg ladder pivoted at the top hangs down from a platform at the circus. A 42.0 kg
trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the
system's natural frequency. The angular frequency (in s1) of the system of ladder and woman is
a. 1.01.
b. 3.07.
c. 4.03.
d. 8.05.
e. 16.2.
ANS: B
PTS: 3
DIF: Challenging
29. Ellen says that whenever the acceleration is directly proportional to the displacement of an object from
its equilibrium position, the motion of the object is simple harmonic motion. Mary says this is true
only if the acceleration is opposite in direction to the displacement. Which one, if either, is correct?
a. Ellen, because 2 is directly proportional to the constant multiplying the displacement and
to the mass.
b. Ellen, because 2 is directly proportional to the mass.
c. Mary, because 2 is directly proportional to the constant multiplying the displacement and
to the mass.
d. Mary, because 2 is directly proportional to the mass.
e. Mary, because the second derivative of an oscillatory function like sin(t) or cos(t) is
always proportional to the negative of the original function.
ANS: E
PTS: 1
DIF: Easy
30. John says that the value of the function cos[(t + T) + ], obtained one period T after time t, is greater
than cos(t + ) by 2. Larry says that it is greater by the addition of 1.00 to cos(t + ). Which one,
if either, is correct?
a. John, because T = 2.
b. John, because T = 1 radian.
c. Larry, because T = 2.
d. Larry, because T = 1 radian.
e. Neither, because cos( + 2) = cos.
ANS: E
PTS: 1
DIF: Easy
31. Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular
velocity onto a diameter of the circle. When this is done, the analog along the diameter of the
acceleration of the particle executing simple harmonic motion is
a. the displacement from the center of the diameter of the projection of the position of the
particle on the circle.
b. the projection along the diameter of the velocity of the particle on the circle.
c. the projection along the diameter of tangential acceleration of the particle on the circle.
d. the projection along the diameter of centripetal acceleration of the particle on the circle.
e. meaningful only when the particle moving in the circle also has a non-zero tangential
acceleration.
ANS: D
PTS: 1
DIF: Easy
32. When a damping force is applied to a simple harmonic oscillator which has angular frequency 0 in
the absence of damping, the new angular frequency  is such that
a.  < 0.
b.  = 0.
c.  > 0.
d. T < 0T0.
e. T > 0T0.
ANS: A
PTS: 1
DIF: Easy
33. When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of
damping, the new period T is such that
a. T < T0.
b. T = T0.
c. T > T0.
d. T < 0T0.
e. T > 0T0.
ANS: C
PTS: 1
DIF: Easy
34. To double the total energy of a mass oscillating at the end of a spring with amplitude A, we need to
a. increase the angular frequency by
.
b. increase the amplitude by
.
c. increase the amplitude by 2.
d. increase the angular frequency by 2.
e.
increase the amplitude by 4 and decrease the angular frequency by
.
ANS: B
PTS: 1
DIF: Easy
35. A damped oscillator is released from rest with an initial displacement of 10.00 cm. At the end of the
first complete oscillation the displacement reaches 9.05 cm. When 4 more oscillations are completed,
what is the displacement reached?
a. 7.41 cm
b. 6.71 cm
c. 6.07 cm
d. 5.49 cm
e. 5.25 cm
ANS: C
PTS: 2
DIF: Average
36. The oscillation of the 2.0-kg mass on a spring is described by
centimeters and t is in seconds. What is the force constant of the spring?
a. 4.0 N/m
b. 0.80 N/m
c. 16 N/m
d. 32 N/m
e. 2.0 N/m
ANS: D
PTS: 2
where x is in
DIF: Average
37. Which of the following combinations of variables results in the greatest period for a pendulum?
a. length = L, mass = M, and maximum angular displacement = 3 degrees
b. length = 2L, mass = M/2, and maximum angular displacement = 1 degree
c. length = 1.5L, mass = 2M, and maximum angular displacement = 2 degrees
d. length =
L, mass =
M, and maximum angular displacement =
degrees
e. length =
L, mass = 4M, and maximum angular displacement = 4 degrees
ANS: B
PTS: 1
DIF: Easy
PROBLEM
38. An automobile (m = 1.00  103 kg) is driven into a brick wall in a safety test. The bumper behaves like
a spring (k = 5.00  106 N/m), and is observed to compress a distance of 3.16 cm as the car is brought
to rest. What was the initial speed of the automobile?
ANS:
2.23 m/s
PTS: 2
DIF: Average
39. The mat of a trampoline is held by 32 springs, each having a spring constant of 5 000 N/m. A person
with a mass of 40.0 kg jumps from a platform 1.93 m high onto the trampoline. Determine the stretch
of each of the springs.
ANS:
9.97 cm
PTS: 3
DIF: Challenging
40. An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to
240 N. What is the equivalent spring constant of the bow, and how much work is done in pulling the
bow?
ANS:
600 N/m, 48 J
PTS: 2
DIF: Average
41. An ore car of mass 4 000 kg starts from rest and rolls downhill on tracks from a mine. A spring with k
= 400 000 N/m is located at the end of the tracks. At the spring's maximum compression, the car is at
an elevation 10 m lower than its elevation at the starting point. How much is the spring compressed in
stopping the ore car? Ignore friction.
ANS:
1.4 m
PTS: 2
DIF: Average
42. The motion of a piston in an auto engine is simple harmonic. If the piston travels back and forth over a
distance of 10 cm, and the piston has a mass of 1.5 kg, what is the maximum speed of the piston and
the maximum force acting on the piston when the engine is running at 4 200 rpm?
ANS:
22 m/s, 14 500 N
PTS: 2
DIF: Average