Deck 15: Oscillations

Question 1

The equation that describes the motion of an object is given by $x = A \cos ( \omega t + \delta )$ . The total distance the object travels during one complete cycle is

A) zero.
B) A.
C) 2A.
D) 4A.

Answer 1

4A.

Question 2

An object is moving with simple harmonic motion. The frequency of the motion of the object is 20.0 MHz. The period of this motion is

A) 50.0 ns.
B) 0.0500 s.
C) 0.500 ms.
D) not determinable from the information given.

Answer 2

50.0 ns.

Question 3

The equation describing the position of an object undergoing simple harmonic motion is $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t - \pi / 2 )$ , where t is in seconds. The angular frequency of the motion is

A) 5 Hz.
B) 5 rads.
C) 10 $\pi$ Hz.
D) 10 $\pi$ rads.

Answer 3

10 $\pi$ rads.

Question 4

The equation describing the position of an object undergoing simple harmonic motion is $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t - \pi / 2 )$ , where t is in seconds. The frequency of the motion is

A) 5 Hz.
B) 5 rads.
C) 10 $\pi$ Hz.
D) 10 $\pi$ rads.

Question 5

The equation describing the position of an object undergoing simple harmonic motion is $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t - \pi / 2 )$ , where t is in seconds. The period of the motion is

A) 0.2 s.
B) 0.1 s.
C) 5 s.
D) 20 s.

Question 6

The equation describing the position of an object undergoing simple harmonic motion is $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t - \pi / 2 )$ , where t is in seconds. The phase of the motion at t = 0.20 seconds is

A) zero.
B) $\pi$ .
C) $\pi$ /2
D)(3/2) $\pi$

Question 7

The equation describing the position of an object undergoing simple harmonic motion is $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t - \pi / 2 )$ , where t is in seconds. The phase constant at t = 0.20 seconds is

A) zero.
B) - $\pi$ .
C) - $\pi$ /2
D)-(3/2) $\pi$

Question 8

The equation describing the position of an object undergoing simple harmonic motion is $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t - \pi / 2 )$ , where t is in seconds. The velocity of the object at t = 0.20 seconds is

A) zero.
B) 13 cm/s.
C)-5.0 cm/s.
D) -160 cm/s.

Question 9

The equation describing the position of an object undergoing simple harmonic motion is $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t - \pi / 2 )$ , where t is in seconds. The acceleration of the object at t = 0.20 seconds is

A) zero.
B) 5000 cm/s².
C) -5000 cm/s².
D) 100 cm/s².

Question 10

When an object undergoing simple harmonic motion is at a turning point, the velocity of the object is

A) at a maximum.
B) always zero.
C) dependent on the overall energy of the system.
D) either positive or negative.

Question 11

An object is oscillating with a frequency of 2.5 Hz and has a maximum displacement of 4.0 cm at t = 0 seconds. The magnitude of the displacement of the object at t = 0.75 seconds is

A) zero.
B) 1.7 cm.
C) 2.8 cm.
D) 3.9 cm.

Question 12

A tuning fork is oscillating with a frequency of 250 Hz and has a maximum displacement of 0.10 mm. The magnitude of the maximum velocity of the tine (the tuning fork's prong) is

A) 0.016 m/s.
B) 0.025 m/s.
C) 0.16 m/s.
D) 0.25 m/s.

Question 13

A tuning fork is oscillating with a frequency of 250 Hz and has a maximum displacement of 0.10 mm. The magnitude of the maximum acceleration of the tine (the tuning fork's prong) is

A) 16 m/s².
B) 25 m/s².
C) 160 m/s².
D) 250 m/s².

Question 14

An object is moving with simple harmonic motion according to the equation $x = ( 5.0 \mathrm {~cm} ) \cos ( 10 \pi t )$ . The time required for the object to move from its initial displacement to 3.5 cm is

A) 15 ms.
B) 25 ms.
C) 1.5 s.
D) 2.5 s.

Question 15

A simple harmonic oscillator consists of a 1.0-kg mass connected to a spring whose force constant is 10.0 N/m. When the system is initially displaced 1.00 cm and released, the period is measured to be 2.0 seconds. If the initial displacement is increased to 2.00 cm, the period is measured as

A) 1.4 s.
B) 2.0 s.
C) 2.8 s.
D) 4.0 s.

Question 16

A simple harmonic oscillator consists of a 1.0-kg mass connected to a spring whose force constant is 10.0 N/m. The frequency of the motion is

A) 0.10 Hz.
B) 0.50 Hz.
C) 1.0 Hz.
D) 5.0 Hz.

Question 17

A pointer on a spring balance oscillates with a period of 0.20 seconds when a 75-N force is initially applied to the pan of the balance. The force constant of the spring is

A) 750 N/m.
B) 1500 N/m.
C) 3500 N/m.
D) 7500 N/m.

Question 18

An individual jumps from a bridge with a bungie cord attached to her foot. She is seen to oscillate with a period of 4.5 seconds. After she stops oscillating, the distance she will extend the cord, relative to the unstretched length of the cord, is

A) 5.0 m.
B) 10 m.
C) 15 m.
D) Hold on; this cannot be answered with the information given.

Question 19

An object is moving with simple harmonic motion with an amplitude of 2.5 cm and a maximum acceleration of 1.0 $\times$ 10² m/s². The frequency of the motion is

A) 10 Hz.
B) 63 Hz.
C) 1.0 $\times$ 10² Hz.
D) 6.3 Hz.

Question 20

Given the following graph, the maximum velocity is

A) 10 cm/s.
B) 20 cm/s.
C) 30 cm/s.
D) 40 cm/s.

Question 21

Given the following graph, the maximum acceleration is

A) 100 cm/s².
B) 200 cm/s².
C) 300 cm/s².
D) 400 cm/s².

Question 22

Given the following graph, the point at which the acceleration is a maximum is

A) A
B) B
C) C
D) not given in the figure.

Question 23

A 2.0-kg mass attached to a spring whose force constant is 10.0 N/m is undergoing simple harmonic motion. If the initial displacement of the mass is 3.0 cm, the total mechanical energy of the system is

A) 2.5 J.
B) 150 mJ.
C) 4.5 mJ.
D) zero.

Question 24

A 2.0-kg mass attached to a spring whose force constant is 10.0 N/m is undergoing simple harmonic motion. If the initial displacement of the mass is 3.0 cm, the maximum potential energy of the system is

A) 2.5 J.
B) 150 mJ.
C) 4.5 mJ.
D) zero.

Question 25

A 2.0-kg mass attached to a spring whose force constant is 10.0 N/m is undergoing simple harmonic motion. If the initial displacement of the mass is 3.0 cm, the maximum kinetic energy of the system is

A) 2.5 J.
B) 150 mJ.
C) 4.5 mJ.
D) zero.

Question 26

The total energy of a spring-mass system is E₀ when the spring is extended to a maximum displacement of x₀. If the maximum displacement is changed to 2x₀, the total energy of the system is

A) 4 E₀.
B) 2 E₀.
C) E₀.
D) (1/2) E₀.

Question 27

The maximum velocity of a spring-mass system is v₀ when the maximum displacement of the mass is x₀. If the maximum displacement is changed to 2x₀, the maximum velocity of the system is

A) (1/2)v₀.
B) v₀.
C) 2v₀.
D) 4v₀.

Question 28

The energy of a spring-mass system is 25.0 J when the maximum displacement is 10.0 cm. If the mass is doubled with the same maximum displacement, the energy of the system is

A) 12.5 J.
B) 17.7 J.
C) 25.0 J.
D) 35.4 J.

Question 29

The energy of a spring-mass system is E₀ when the maximum displacement is x₀. If the total mechanical energy of the system is held constant and the mass is increased by a factor of two, the maximum velocity of the system is

A) (1/2) v₀.
B) (0.707) v₀.
C) v₀.
D) (1.414) v₀.

Question 30

The physical interpretation of the quality factor, Q, of a harmonic oscillator is

A) that it is related to the amplitude enhancement for a system driven by an external force at resonance.
B) roughly coincident with the number of cycles the oscillator completes before the oscillations damp away significantly.
C) a factor that is related to the energy lost per cycle.
D) related to all of the above statements.

Question 31

The energy of a harmonic oscillator is reduced by 2.0% each cycle. The quality factor, Q, for this system is

A) 5.
B) 31.
C) 50.
D) 310.

Question 32

The displacement of a spring mass is reduced by 5.0% each cycle. The quality factor, Q, for this system is

A) zero.
B) 31.
C) 64.
D) 130.

Question 33

A spring-mass system that has a spring constant of 5.0 N/m is subject to a periodic restoring force of 0.015 N at a frequency that is very close to the natural resonance of the system. If the amplitude of the motion of the mass at this driving frequency is 3.0 cm, the quality factor, Q, is

A) zero.
B) 5.
C) 10.
D) 500.

Question 34

A piano string tuned to 440 cycles per second has a quality factor of 3000. The fraction of the original energy that remains after 20 cycles is

A) 4%.
B) 78%.
C) 96%.
D) 100%.

Question 35

A student has a spring, whose spring constant is 5.0 N/m, with a 1.0-kg mass attached to it that is hanging freely. The quality factor of the system is 50. She wishes to have the maximum displacement of the system be 7.5 cm. The force and frequency required to produce this motion are

A) 0.0075 N and 2.8 s.
B) 0.0075 N and 1.4 s.
C) 19 N and 2.8 s.
D) 19 N and 1.4 s.

Question 36

A mass is lying on a flat surface where the coefficient of friction between the surface and the mass is $\mu$ . The mass is connected to a spring that produces a force equal to -kx, where k is the spring constant and x is the displacement from the equilibrium position. The equation of motion of the mass when it is displaced a distance x₀ is:

A) $m \ddot { x } = - k x - \mu m g$
B) $m \ddot { x } = + k x + \mu m g$
C) $m \ddot { x } = k x - \mu m g$
D) $m \ddot { x } = - k x + \mu m g$

Question 37

A uniform meterstick (considered to be a uniform rod) that is 1.00 m in length is connected to a pivot at the 0.0 cm mark. The period of the motion for small oscillations is

A) 1.42 s.
B) 1.64 s.
C) 1.74 s.
D) 2.01 s.

Question 38

A uniform meterstick (considered to be a uniform rod) that is 1.00 m in length is connected to a pivot at the 10.0-cm mark. The period of the motion for small oscillations is

A) 1.25 s.
B) 1.40 s.
C) 1.74 s.
D) 2.01 s.

Question 39

A uniform meterstick (considered to be a uniform rod) that is 1.00 m in length is connected to a pivot at the 50.0-cm mark. The period of the motion for small oscillations is

A) 0.42 s.
B) 0.74 s.
C) 0.82 s.
D) 1.00 s.

Question 40

A small ball with radius 1.00 cm is placed inside a large bowl whose radius is 1.50 m. If the ball is given a small displacement from the bottom of the bowl, the period of the motion is

A) 2.85 s.
B) 2.90 s.
C) 2.95 s.
D) 3.00 s.

Question 41

Two springs are connected in parallel to a 1.0-kg mass. If the spring constants are k₁ = 15.0 N/m and k₂ = 10.0 N/m, the period of the motion is

A) 1.26 s.
B) 2.56 s.
C) 2.81 s.
D) 3.61 s.

Question 42

Two springs are connected in series to a 1.0-kg mass. If the spring constants are k₁ = 15.0 N/m and k₂ = 10.0 N/m, the period of the motion is

A) 1.26 s.
B) 2.56 s.
C) 2.81 s.
D) 3.61 s.

Question 43

The position of a 2.0-kg mass connected to a spring whose constant is 15 N/m is given by $x = A \cos ( \omega t - \delta )$ , where A = 25 cm and $\delta$ = $\pi$ /2. The kinetic energy of the mass at time t = 0 is

A) 0 J.
B) 0.47 J.
C) 0.50 J.
D) 1.0 J.

Question 44

The position of a 2.0-kg mass connected to a spring whose constant is 15 N/m is given by $x = A \cos ( \omega t - \delta )$ , where A = 25 cm and $\delta$ = $\pi$ /2. The potential energy of the mass at time t = 0 is

A) 0 J.
B) 0.47 J.
C) 0.50 J.
D) 1.0 J.

Question 45

The position of a 2.0-kg mass connected to a spring whose constant is 15 N/m is given by $x = A \cos ( \omega t - \delta )$ , where A = 25 cm and $\delta$ = $\pi$ /2. The total mechanical energy of the mass at time t = 0 is

A) 0 J.
B) 0.47 J.
C) 0.50 J.
D) 1.0 J.

Question 46

The position of a 2.0-kg mass connected to a spring whose constant is 15 N/m is given by $x = A \cos ( \omega t - \delta )$ , where A = 25 cm and $\delta$ = $\pi$ /2. The potential energy of the mass at time t = 0.30 seconds is

A) 0 J.
B) 0.26 J.
C) 0.31 J.
D) 0.34 J.

Question 47

The position of a 2.0 kg mass connected to a spring whose constant is 15 N/m is given by $x = A \cos ( \omega t - \delta )$ , where A = 25 cm and $\delta$ = $\pi$ /2. The kinetic energy of the mass at time t = 0.30 seconds is

A) 0 J.
B) 0.16 J.
C) 0.21 J.
D) 0.47 J.

Question 48

The position of a 2.0-kg mass connected to a spring whose constant is 15 N/m is given by $x = A \cos ( \omega t - \delta )$ , where A = 25 cm and $\delta$ = $\pi$ /2. The total mechanical energy of the mass at time t = 0.30 seconds is

A) 0 J.
B) 0.34 J.
C) 0.47 J.
D) 1.0 J.

Question 49

The position of a 2.0-kg mass connected to a spring whose constant is 15 N/m is given by $x = A \cos ( \omega t - \delta )$ , where A = 25 cm and $\delta$ = $\delta$ /2. If the spring has a quality factor of 50 the velocity of the mass at time t = 0.50 seconds is

A) 0 m/s.
B) 0.32 m/s.
C) 0.41 m/s.
D) 0.64 m/s.