Question 1

An object of mass m = 700 g is attached to a spring. Its position is described by x = (0.15 m)cos(0.8ðt). What is the spring constant?

Accepted Answer

A) 1.76 N/m 
B) 4.42 N/m 
C) 44.2 N/m 
D) 4420 N/m 
A) 1.76 N/m 
B) 4.42 N/m 
C) 44.2 N/m 
D) 4420 N/m

Question 2

For an object oscillating on a spring, when is the velocity of the object the largest?

Accepted Answer

A) when potential energy is minimal 
B) when potential energy is maximal 
C) when displacement is farthest away from equilibrium 
D) when acceleration is maximal 
A) when potential energy is minimal 
B) when potential energy is maximal 
C) when displacement is farthest away from equilibrium 
D) when acceleration is maximal

Question 3

Which of these statements can be applied to plastic deformation of an object?

Accepted Answer

A) It permanently changes the shape of an object. 
B) The object returns to the original shape once the pressure stops. 
C) It always occurs just before the object breaks. 
D) A material experiencing it responds to stress in a linear fashion. 
A) It permanently changes the shape of an object. 
B) The object returns to the original shape once the pressure stops. 
C) It always occurs just before the object breaks. 
D) A material experiencing it responds to stress in a linear fashion.

Question 4

Figure 13.4
The amplitude as a function of driving frequency for three oscillators.  
-Figure 13.4 shows the response of three oscillators to a driving frequency. The amplitudes are plotted as a function of frequency. If each of these three oscillators is started and then left as a free oscillator, discuss which will oscillate longest, which shortest, and why?

Accepted Answer

Oscillator 1 will oscillate shortest and

Question 5

The total energy of a body attached on a horizontal spring is largest in equilibrium.

Accepted Answer

A) True 
 B)False

Question 6

Both elastic and plastic deformations are reversible. The only difference between the two is that elastic material responds to stress in a linear fashion, and plastic responds in a non-linear fashion.

Accepted Answer

A) True 
 B)False

Question 7

For an object attached to a horizontal spring, what is the relationship between kinetic (Ekin) and potential (Epot) energy of the object when positioned at the point where displacement is exactly half the amplitude?

Accepted Answer

A) Ekin = 3Epot 
B) Epot = 3Ekin 
C) Ekin = 2Epot 
D) Epot = 2Ekin 
A) Ekin = 3Epot 
B) Epot = 3Ekin 
C) Ekin = 2Epot 
D) Epot = 2Ekin

Question 8

The oscillatory motions of a mass on a horizontal spring and on an identical vertical spring are NOT the same because the force of gravity (weight) is acting in a vertical motion.

Accepted Answer

A) True 
 B)False

Question 9

A restoring force is always directed opposite to displacement.

Accepted Answer

A) True 
 B)False

Question 10

The total energy of a water molecule in the ground state is 9.2 × 10-20 J. Find the amplitude and maximal velocity of vibration of a hydrogen atom. Compare the amplitude to the length of the O-H bond (9.6 × 10-11 m). The mass of a hydrogen atom is m = 1.67 × 10-27 kg. The spring constant for the H-O bond is k = 780 N/m.

Accepted Answer

A = 1.5 × 10^-11 m (16%

Question 11

A Blue Elgiloy wire with a Young's modulus of Y = 1.6 × 1011 Pa is used to press a tooth for correction of position. The wire is 3 cm long, has a diameter of 0.2 mm, bends under an angle of 140° where it presses the tooth, and stretches by 0.08 mm. What is the force exerted on the tooth? Assume that that tooth width is negligible so that the wire bends making an angle 140°.

Accepted Answer

9.2 N
RAT:

Question 12

Which of these quantities does NOT have to be conserved in the process of stretching of an extended object?

Accepted Answer

A) volume 
B) mass 
C) length 
D) density 
A) volume 
B) mass 
C) length 
D) density

Question 13

If you increase the displacement of a spring from an equilibrium position by 2 times, how will its elastic potential energy change?

Accepted Answer

A) It will increase by 2 times. 
B) It will decrease by 2 times. 
C) It will increase by 4 times. 
D) It will decrease by 4 times. 
A) It will increase by 2 times. 
B) It will decrease by 2 times. 
C) It will increase by 4 times. 
D) It will decrease by 4 times.

Question 14

You attach a mass to a spring and let it oscillate. If you attach the same mass to another spring that has a spring constant that is 4 times larger than the first spring, how does the linear frequency of oscillations change?

Accepted Answer

A) increases by 2 times 
B) increases by 4 times 
C) increases by   times 
D) decreases by 2 times 
A) increases by 2 times 
B) increases by 4 times 
C) increases by   times 
D) decreases by 2 times

Question 15

Figure 13.1
​   ​
The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction.
-In Fig. 13.1, at which position does the object reach maximum kinetic energy?

Accepted Answer

A) (i) 
B) (ii) 
C) (iii) 
D) (iv) 
A) (i) 
B) (ii) 
C) (iii) 
D) (iv)

Question 16

If you double the amplitude of a simple harmonic oscillator, how is maximum velocity going to change?

Accepted Answer

A) double 
B) increase by 4 times 
C) decrease by 2 times 
D) decrease by 4 times 
A) double 
B) increase by 4 times 
C) decrease by 2 times 
D) decrease by 4 times

Question 17

Angular frequency (the change of angle in an interval of time) is expressed in either degrees per second or radians per second.

Accepted Answer

A) True 
 B)False

Question 18

A system is in resonance when an external harmonic excitation causes it to respond with maximum __________.

Accepted Answer

A) amplitude 
B) frequency 
C) wavelength 
D) period 
A) amplitude 
B) frequency 
C) wavelength 
D) period

Question 19

A force that causes an oscillating system to slow down is called a

Accepted Answer

A) restoring force. 
B) Hooke's force. 
C) damping force. 
D) driving force. 
A) restoring force. 
B) Hooke's force. 
C) damping force. 
D) driving force.

Question 20

You want to measure the weight of a bag of fruit. When you place the bag on a scale, it shows harmonic oscillation around 29.4 N, 3 oscillations per second. What is the spring constant of the scale?

Accepted Answer

k = 1065 N

Exam 13: Elasticity and Vibrations

An object of mass m = 700 g is attached to a spring. Its position is described by x = (0.15 m)cos(0.8ðt). What is the spring constant?

For an object oscillating on a spring, when is the velocity of the object the largest?

Which of these statements can be applied to plastic deformation of an object?

The total energy of a body attached on a horizontal spring is largest in equilibrium.

Both elastic and plastic deformations are reversible. The only difference between the two is that elastic material responds to stress in a linear fashion, and plastic responds in a non-linear fashion.

For an object attached to a horizontal spring, what is the relationship between kinetic (Ekin) and potential (Epot) energy of the object when positioned at the point where displacement is exactly half the amplitude?

The oscillatory motions of a mass on a horizontal spring and on an identical vertical spring are NOT the same because the force of gravity (weight) is acting in a vertical motion.

A restoring force is always directed opposite to displacement.

Which of these quantities does NOT have to be conserved in the process of stretching of an extended object?

If you increase the displacement of a spring from an equilibrium position by 2 times, how will its elastic potential energy change?

You attach a mass to a spring and let it oscillate. If you attach the same mass to another spring that has a spring constant that is 4 times larger than the first spring, how does the linear frequency of oscillations change?

Figure 13.1 ​ ​ The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction. -In Fig. 13.1, at which position does the object reach maximum kinetic energy?

If you double the amplitude of a simple harmonic oscillator, how is maximum velocity going to change?

Angular frequency (the change of angle in an interval of time) is expressed in either degrees per second or radians per second.

A system is in resonance when an external harmonic excitation causes it to respond with maximum __________.

A force that causes an oscillating system to slow down is called a

You want to measure the weight of a bag of fruit. When you place the bag on a scale, it shows harmonic oscillation around 29.4 N, 3 oscillations per second. What is the spring constant of the scale?

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For an object attached to a horizontal spring, what is the relationship between kinetic (E_kin) and potential (E_pot) energy of the object when positioned at the point where displacement is exactly half the amplitude?

Figure 13.1 The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction. -In Fig. 13.1, at which position does the object reach maximum kinetic energy?