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Energy in SHM: In simple harmonic motion, the speed is greatest at that point in the cycle when


A) the magnitude of the acceleration is a maximum.
B) the displacement is a maximum.
C) the magnitude of the acceleration is a minimum.
D) the potential energy is a maximum.
E) the kinetic energy is a minimum.

F) A) and B)
G) C) and D)

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Simple harmonic motion: The simple harmonic motion of an object is described by the graph shown in the figure. What is the equation for the position x(t) of the object as a function of time t? Simple harmonic motion: The simple harmonic motion of an object is described by the graph shown in the figure. What is the equation for the position x(t)  of the object as a function of time t?   A)  x(t)  = (4.0 cm) sin[(2π/8.0 s) t + π/3.0] B)  x(t)  = (4.0 cm) cos[(2π/8.0 s) t + 2π/3.0] C)  x(t)  = (4.0 cm) cos[(2π/8.0 s) t + π/3.0] D)  x(t)  = (4.0 cm) cos[(2π/8.0 s) t - π/3.0] E)  x(t)  = (8.0 cm) cos[(2π/8.0 s) t + π/3.0]


A) x(t) = (4.0 cm) sin[(2π/8.0 s) t + π/3.0]
B) x(t) = (4.0 cm) cos[(2π/8.0 s) t + 2π/3.0]
C) x(t) = (4.0 cm) cos[(2π/8.0 s) t + π/3.0]
D) x(t) = (4.0 cm) cos[(2π/8.0 s) t - π/3.0]
E) x(t) = (8.0 cm) cos[(2π/8.0 s) t + π/3.0]

F) A) and E)
G) A) and B)

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Resonance: An object of mass of 2.0 kg hangs from an ideal massless spring with a spring constant of 50 N/m. An oscillating force F = (4.8 N) cos[(3.0 rad/s) t] is applied to the object. What is the amplitude of the resulting oscillations? You can neglect damping.


A) 0.15 m
B) 0.30 m
C) 1.6 m
D) 2.4 m
E) 0.80 m

F) C) and E)
G) A) and B)

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Simple harmonic motion: The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm) cos[(1.26s-1)t]. At time t = 0.815 s, (a) how fast is the object moving? (b) what is the magnitude of the acceleration of the object?

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(a) 13.3 c...

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Mass on a spring: In the figure, two masses, M = 16 kg and m = 12.8 kg, are connected to a very light rigid bar and are attached to an ideal massless spring of spring constant 100 N/m. The system is set into oscillation with an amplitude of 78 cm. At the instant when the acceleration is at its maximum, the 16-kg mass separates from the 12.8-kg mass, which then remains attached to the spring and continues to oscillate. What will be the amplitude of oscillation of the 12.8-kg mass? Mass on a spring: In the figure, two masses, M = 16 kg and m = 12.8 kg, are connected to a very light rigid bar and are attached to an ideal massless spring of spring constant 100 N/m. The system is set into oscillation with an amplitude of 78 cm. At the instant when the acceleration is at its maximum, the 16-kg mass separates from the 12.8-kg mass, which then remains attached to the spring and continues to oscillate. What will be the amplitude of oscillation of the 12.8-kg mass?   A)  78 cm B)  62 cm C)  35 cm D)  98 cm E)  180 cm


A) 78 cm
B) 62 cm
C) 35 cm
D) 98 cm
E) 180 cm

F) B) and C)
G) B) and E)

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Simple harmonic motion: Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s?


A)
Simple harmonic motion: Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s? A)    B)    C)    D)    E)
B)
Simple harmonic motion: Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s? A)    B)    C)    D)    E)
C)
Simple harmonic motion: Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s? A)    B)    C)    D)    E)
D)
Simple harmonic motion: Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s? A)    B)    C)    D)    E)
E)
Simple harmonic motion: Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s? A)    B)    C)    D)    E)

F) A) and C)
G) C) and D)

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Energy in SHM: A 0.50-kg object is attached to an ideal massless spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? (b) At what location are the kinetic energy and the potential energy of the system the same?

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(a) 0.24 m...

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Simple harmonic motion: A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. (a) What is the maximum speed of the needle? (b) What is the maximum acceleration of the needle?

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(a) 20.3 c...

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Energy in SHM: If we double only the amplitude of a vibrating ideal mass-and-spring system, the mechanical energy of the system


A) increases by a factor of Energy in SHM: If we double only the amplitude of a vibrating ideal mass-and-spring system, the mechanical energy of the system A)  increases by a factor of   . B)  increases by a factor of 2. C)  increases by a factor of 3. D)  increases by a factor of 4. E)  does not change. .
B) increases by a factor of 2.
C) increases by a factor of 3.
D) increases by a factor of 4.
E) does not change.

F) B) and D)
G) D) and E)

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Energy in SHM: A 1.5-kg mass attached to an ideal massless spring with a spring constant of 20.0 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the mass is released from rest at x = 10.0 cm. (That is, the spring is stretched by 10.0 cm.) (a) Find the frequency of the oscillations. (b) Determine the maximum speed of the mass. At what point in the motion does the maximum speed occur? (c) What is the maximum acceleration of the mass? At what point in the motion does the maximum acceleration occur? (d) Determine the total energy of the oscillating system. (e) Express the displacement x as a function of time t.

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(a) 0.58 Hz
(b) 0.37 m/s, at ...

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Simple pendulum: A frictionless pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical because the period is independent of the amplitude and mass.

A) True
B) False

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Mass on a spring: A mass M is attached to an ideal massless spring. When this system is set in motion, it has a period T. What is the period if the mass is doubled to 2M?


A) 2T
B) T/2
C) Mass on a spring: A mass M is attached to an ideal massless spring. When this system is set in motion, it has a period T. What is the period if the mass is doubled to 2M? A)  2T B)  T/2 C)    T D)  4T E)  T T
D) 4T
E) T

F) B) and D)
G) B) and C)

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Damped harmonic motion: A 25 kg object is undergoing lightly damped harmonic oscillations. If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s, what is the value of the damping constant b?


A) 31 kg/s
B) 34 kg/s
C) 37 kg/s
D) 40 kg/s

E) A) and B)
F) A) and C)

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Damped harmonic motion: An ideal massless spring with a spring constant of 2.00 N/m is attached to an object of 75.0 g. The system has a small amount of damping. If the amplitude of the oscillations decreases from 10.0 mm to 5.00 mm in 15.0 s, what is the magnitude of the damping constant b?


A) 0.00693 kg/s
B) 0.0462 kg/s
C) 0.00762 kg/s
D) 0.0100 kg/s
E) 0.00857 kg/s

F) None of the above
G) A) and B)

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Energy in SHM: An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B. When the kinetic energy of the object is a minimum, the object is located


A) at either A or B.
B) midway between A and B.
C) 1/3 of the distance from A to B.
D) 1/4 of the distance from A to B.
E) 1/ Energy in SHM: An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B. When the kinetic energy of the object is a minimum, the object is located A)  at either A or B. B)  midway between A and B. C)  1/3 of the distance from A to B. D)  1/4 of the distance from A to B. E)  1/   times the distance from A to B. times the distance from A to B.

F) A) and B)
G) B) and D)

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Damped harmonic motion: A 5.0-kg block is attached to an ideal massless spring whose spring constant is 125 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a position at x = +0.687 m and is released from rest. The block then executes lightly damped oscillation along the x-axis, and the damping force is proportional to the velocity. When the block first returns to x = 0.00 m, its x component of velocity is -2.0 m/s and its x component of acceleration is +5.6 m/s2. (a) What is the magnitude of the acceleration of the block upon release at x = +0.687 m. (b) Find the damping constant b.

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(a) 17.2 m...

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Energy in SHM: A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is Energy in SHM: A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is   The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the displacement is   what is the kinetic energy of the block? A)  0.44 J B)  0.41 J C)  0.46 J D)  0.49 J E)  0.52 J The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the displacement is Energy in SHM: A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is   The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the displacement is   what is the kinetic energy of the block? A)  0.44 J B)  0.41 J C)  0.46 J D)  0.49 J E)  0.52 J what is the kinetic energy of the block?


A) 0.44 J
B) 0.41 J
C) 0.46 J
D) 0.49 J
E) 0.52 J

F) A) and B)
G) A) and C)

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Mass on a spring: A mass M is attached to an ideal massless spring. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is increased to 2A?


A) 2T
B) T/2
C) Mass on a spring: A mass M is attached to an ideal massless spring. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is increased to 2A? A)  2T B)  T/2 C)    T D)  4T E)  T T
D) 4T
E) T

F) B) and E)
G) A) and E)

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Mass on a spring: A 56.0 kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant of the bungee cord, assuming it has negligible mass compared to that of the jumper?


A) 17.6 N/m
B) 21.1 N/m
C) 28.2 N/m

D) A) and C)
E) All of the above

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Resonance: In designing buildings to be erected in an area prone to earthquakes, what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?


A) The natural frequency of the building should be exactly the same as typical earthquake frequencies.
B) The natural frequency of the building should be very different from typical earthquake frequencies.
C) The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly higher.
D) The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly lower.

E) A) and B)
F) A) and C)

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