Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) A 4.8-kg block attached to a spring executes simple harmonic motion on a frictionless horizontal
surface. At time t = 0 s, the block has a displacement of -0.50 m, a velocity of -0.80 m/s, and an
acceleration of +8.3 m/s2. The force constant of the spring is closest to:
A) 56 N/m
B) 62 N/m
C) 73 N/m
D) 80 N/m
E) 67 N/m
2) A 3.4-kg block attached to a spring executes simple harmonic motion on a frictionless horizontal
surface. At time t = 0 s, the block has a displacement of -0.50 m, a velocity of -0.80 m/s, and an
acceleration of +3.8 m/s2. The amplitude of the motion is closest to:
A) 0.80 m
B) 3.8 m
C) 0.88 m
D) 0.58 m
1)
2)
E) 0.72 m
3) A 1.5-kg block on a horizontal frictionless surface is attached to a spring whose force constant is
220 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement
x = +0.080 m and is released from rest. The block then executes simple harmonic motion along
the x-axis (horizontal). The displacement of the block at time t = 0.70 s is closest to:
A) 0.07 m
B) -0.5 m
C) 0.04 m
D) -0.04 m
E) -0.07 m
3)
4) A 1.6-kg block on a horizontal frictionless surface is attached to a spring whose force constant is
190 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement
x = +0.080 m and is released from rest. The block then executes simple harmonic motion along
the x-axis (horizontal). The velocity of the block at time t = 0.40 s is closest to:
A) -0.8 m/s
B) -0.3 m/s
C) 0.8 m/s
D) 0.3 m/s
E) zero
4)
5) A 0.13-kg block on a horizontal frictionless surface is attached to a spring whose force constant
is 500 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement
x = +0.080 m and is released from rest. The block then executes simple harmonic motion along
the x-axis (horizontal). When the displacement is x = 0.018 m, the kinetic energy of the block is
closest to:
A) 1.5 J
B) 1.4 J
C) 1.7 J
D) 1.8 J
E) 1.6 J
5)
6) A 0.028-kg block on a horizontal frictionless surface is attached to a spring whose force constant
is 170 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement
x = +0.080 m and is released from rest. The block then executes simple harmonic motion along
the x-axis (horizontal). When the displacement is x = -0.054 m, the acceleration of the block is
closest to:
A) 250 m/s2
B) 970 m/s2
C) 160 m/s2
D) 820 m/s2
E) 330 m/s2
6)
7) A 0.068-kg block on a horizontal frictionless surface is attached to a spring whose force constant
is 390 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement
x = +0.080 m and is released from rest. The block then executes simple harmonic motion along
the x-axis (horizontal). The maximum elastic potential energy of the system is closest to:
A) 1.1 J
B) 1.2 J
C) 1.4 J
D) 1.5 J
E) 1.6 J
7)
1
Figure 13.1
8) In Fig. 13.1, two masses, M = 10 kg and m = 8 kg, are attached to a spring of spring constant
100 N/m. The system is set into oscillation with an amplitude of 58 cm. At the instant when the
acceleration is at maximum, the 10-kg mass separates from the 8-kg mass, which then remains
attached to the spring and continues to oscillate. The amplitude of oscillation of the 8-kg mass
will be:
A) 46 cm
B) 58 cm
C) 130 cm
D) 73 cm
E) 26 cm
8)
9) For an object undergoing simple harmonic motion,
A) the acceleration is greatest when the speed is greatest.
B) the acceleration is greatest when the displacement is greatest.
C) the displacement is greatest when the speed is greatest.
9)
D) the total energy oscillates at frequency f = 1
2π
k .
m
E) the maximum potential energy is larger than the maximum kinetic energy.
10) A particle is in simple harmonic motion along the x-axis with a period of 1.4 s and an amplitude
of 0.78 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is at
x = +0.47 m and it is moving in the negative x-direction. The magnitude of the velocity of the
particle, at time t = 0 s , is closest to:
A) 2.8 m/s
B) 4.6 m/s
C) 4.1 m/s
D) 5.5 m/s
E) 3.5 m/s
10)
11) A particle is in simple harmonic motion along the x-axis with a period of 7.7 s and an amplitude
of 0.51 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is at
x = +0.36 m and it is moving in the negative x-direction. The x-component of the acceleration,
at time t = 0 , is closest to:
A) -0.34
B) 0.34
C) -0.24
D) 0.24
E) zero
11)
12) A particle is in simple harmonic motion along the x-axis with a period of 3.7 s and an amplitude
of 0.64 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is at
x = +0.38 m and it is moving in the negative x-direction. The time interval required for the
particle to reach x = - 0.64 m from its initial position at t = 0 s is closest to:
A) 2.6 s
B) 1.3 s
C) 2.0 s
D) 2.3 s
E) 1.6 s
12)
13) A particle is in simple harmonic motion along the x-axis with a period of 3.5 s and an amplitude
of 0.32 m. The equilibrium position of the particle is at x = 0. At time t = 0, the particle is at
x = +0.26 m and it is moving in the negative x-direction. At time t = 0, the ratio of the potential
energy to the total mechanical energy is closest to:
A) 0.72
B) 0.64
C) 0.80
D) 1.1
E) 1.4
13)
2
Situation 13.1
A 0.90-kg solid disk has a radius of 10 cm and a thickness of 1.0 cm. The disk is used as a balance wheel in a mechanism
and the torsion constant is 0.020 N ∙ m/rad.
14) In Situation 13.1, the period of oscillation of the wheel is closest to:
A) 4.2 s
B) 1.5 s
C) 2.1 s
D) 3.0 s
14)
E) 1.1 s
15) In Situation 13.1, the torque required to hold the wheel at a 90° angular displacement from
equilibrium is closest to:
A) 0.05 N ∙ m
B) 0.01 N ∙ m
C) 0.04 N ∙ m
D) 0.03 N ∙ m
E) 0.02 N ∙ m
15)
Figure 13.2
16) In Fig. 13.2, a mass of 2 kg is attached to three springs of spring constants 1 N/m, 2 N/m, and
3 N/m. When the mass is at rest the springs are unstretched. For this system:
A) !2 = 3/2 rad/s2
16)
B) !2 = 1 rad/s2
C) !2 = 1/2 rad/s2
D) !2 = 3 rad/s2
E) !2 = 2 rad/s2
17) It has been suggested that a possible transportation system to connect two cities such as Boston
and Washington, D.C., might function like this: Drill a tunnel straight from Boston to
Washington. A car released in Boston would fall under the influence of gravity, gaining speed,
and then finally coasting back to the surface at Washington. The only expenditure of energy
required would be that to overcome friction, and this could be reduced by using an evacuated
tunnel or magnetic levitation of the train or other possible techniques. Assuming the density of
the earth is constant (it isn't), and using only the value of the acceleration of gravity at the earth's
surface (9.8 m/s2) and the radius of the earth (6380 km) determine how long it would take to
travel between any two cities via a straight tunnel. The result, rather surprisingly, is about:
A) 58 minutes
B) 42 minutes
C) 1 hour 23 minutes
D) 2 hours 54 minutes
E) 6 hours 33 minutes
3
17)
Situation 13.2
The x-component of the velocity of an object vibrating along the x-axis obeys the equation vx(t) = (0.445 m/s) sin[(25.4
rad/s)t + 0.223].
18) In Situation 13.2, the amplitude of the motion is closest to:
A) 0.445 m
B) 0.223 m
C) 0.0175 m
18)
D) 0.247 m
E) 25.4 m
19) In Situation 13.2, the maximum acceleration of the vibrating object is closest to:
A) 287 m/s2
19)
B) 0.286 m/s2
C) 25.4 m/s2
D) 0.445 m/s2
E) 11.3 m/s2
Situation 13.3
The angle with the vertical of a swinging simple pendulum obeys the equation
!(t) = (0.150 rad) cos[(2.85 rad/s)t + 1.66].
20) In Situation 13.3, the length of the pendulum is closest to:
A) 3.44 m
B) 0.15 m
C) 1.21 m
20)
D) 0.83 m
E) 2.02 m
21) In Situation 13.3, the mass of the swinging bob at the end of the pendulum is closest to:
A) 0.454 kg
B) 2.85 kg
C) 0.150 kg
D) 1.66 kg
E) It cannot be determined from the information given.
21)
22) A mass at the end of an ideal spring vibrates with period T. If you double the mass, by what
factor must you change the force constant of the spring so that the period of vibration will now
be 2T?
A) Decrease it by a factor of 2.
B) Decrease it by a factor of 2.
C) Increase it by a factor of 2.
D) Decrease it by a factor of 4.
E) Increase it by a factor of 2.
22)
23) A 2.00-kg mass is attached to an ideal horizontal spring of force constant 100.0 N/m and is at
rest on a frictionless horizontal table. The spring is aligned along the x-axis and is fixed to a peg
in the table. Suddenly this mass is struck by another 2.00-kg mass traveling along the x-axis at
3.00 m/s, and the two masses stick together. For the oscillations that result from this collision,
the amplitude and period are closest to:
A) 0.424 m, 1.26 s
B) 0.300 m, 1.26 s
C) 0.300 m, 0.889 s
D) 0.424 m, 0.889 s
E) 0.424 m, 5.00 s
23)
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24) A meter stick is freely pivoted about the 20-cm mark. The frequency of small amplitude
oscillations is closest to:
A) 1.5 Hz
B) 0.7 Hz
C) 0.5 Hz
D) 1.2 Hz
E) 0.9 Hz
24)
25) A coin is placed on a platform attached to a spring that oscillates vertically in simple harmonic
motion. The amplitude of the displacement is 1.20 cm. What is the maximum frequency for
which the coin will always remain in contact with the platform?
A) 6.89 Hz
B) 8.75 Hz
C) 12.2 Hz
D) 4.55 Hz
E) 2.25 Hz
25)
26) If both the mass of a simple pendulum and its length are doubled, the period will
A) be unchanged.
B) increase by a factor of 2.
C) increase by a factor of 0.71.
D) increase by a factor of 4.
E) increase by a factor of 1.4
26)
27) What happens when a periodic driving force is applied to a vibrating system?
A) The system will vibrate at the frequency of the driving force.
B) The system will stop vibrating and finally come to a stop.
C) It will vibrate at some multiple of the driving frequency (called a harmonic or "overtone").
D) The system will vibrate at its natural frequency.
E) The system will exhibit chaotic motion.
27)
Situation 13.4
A 5.0-kg block is attached to a spring whose force constant is 125 N/m. The block is pulled from its equilibrium position
at x = 0 m to a position at x = +0.687 m and is released from rest. The block then executes damped oscillation along the
x-axis. The damping force is proportional to the velocity. When the block first returns to x = 0 m, its x-component of
velocity is -2.0 m/s and its x-component of acceleration is +5.6 m/s2.
28) In Situation 13.4, the magnitude of the acceleration of the block upon release at x = +0.687 m is
closest to:
A) 16.4 m/s2
28)
B) 19.6 m/s2
C) 18.0 m/s2
D) 18.8 m/s2
E) 17.2 m/s2
29) In Situation 13.4, the damping coefficient b is closest to:
A) 14 kg/s2
B) 22 kg/s2
C) 16 kg/s2
29)
D) 18 kg/s2
E) 20 kg/s2
30) In Situation 13.4, the work done by the damping force during the travel of the block from
x = +0.687 m to x = 0 m is closest to:
A) -20 J
B) -30 J
C) -25 J
D) -15 J
E) -10 J
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30)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
31) An object of mass 6.8 kg is attached to a spring of force constant 1780 N/m. The object is
set into simple harmonic motion, with an initial velocity of ! o = 3.2 m/s and an initial
displacement of x o = 0.14 m. Calculate the maximum velocity the object has during its
motion.
31)
32) An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and
amplitude A = 0.12 m. At t = 0 the object is at x = 0. How long does it take the object to
go from x = 0 to x = 0.024 m?
32)
33) A large stick is pivoted about one end and allowed to swing back and forth as a physical
pendulum. The mass of the stick is 5.20 kg and its center of gravity (found by finding its
balance point) is 2.00 m from the pivot. If the period of the swinging stick is
4.10 seconds, what is its moment of inertia, about an axis through the pivot?
33)
34) A 4.50-kg weight hangs from a vertical massless ideal spring. When set in vertical
motion, the weight obeys the equation y(t) = (6.20 cm) cos[(2.74 rad/s)t - 1.40]. Find: (a)
the time for this weight to vibrate one complete cycle, (b) the maximum speed and
maximum acceleration of the weight, (c) the total distance the weight moves through in
one cycle, (d) the maximum kinetic energy of the weight, and (e) the force constant of
the spring.
34)
Figure 13.3
35) In Fig. 13.3, a 0.24-kg ball is suspended from a string 9.79 m long and is pulled slightly
to the left. As the ball swings through the lowest part of its motion it encounters a spring
attached to the wall. The spring pushes against the ball and eventually the ball is
returned to its original starting position. Find the time for one complete cycle of this
motion if the spring constant is 21 N/m. (Assume that once the pendulum ball hits the
spring there is no effect due to the vertical movement of the ball.)
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35)
Answer Key
Testname: UNTITLED1
1) D
2) D
3) D
4) C
5) A
6) E
7) B
8) B
9) B
10) A
11) C
12) B
13) B
14) B
15) D
16) D
17) B
18) C
19) E
20) C
21) E
22) C
23) B
24) B
25) D
26) E
27) A
28) E
29) A
30) A
31) 3.9 m/s
32) 0.0033 seconds
33) 43.4 kg ∙ m2
34) (a) 2.29 s (b) .170 m/s, 0.465 m/s2 (c) 24.8 cm (d) 0.0649 J (e) 33.8 N/m
35) 3.5 s
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