Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

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 phase constant at t = 0.20 seconds is

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Given the following graph, the maximum acceleration is

Accepted Answer

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

Question 7

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:

Accepted Answer

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)  $m \ddot { x } = - k x + \mu m g$ 
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 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 angular frequency of the motion is

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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. 
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 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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

Exam 15: Oscillations

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

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

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

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

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

Given the following graph, the maximum acceleration is

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

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

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

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

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

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

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 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 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 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 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

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

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

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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

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

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

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

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

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

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

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

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