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Exam 14: Oscillations

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Question 51

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A 2.0-kg block on a frictionless table is connected to two springs whose opposite ends are fixed to walls, as shown in the figure. The springs have force constants (spring constants) k₁ and k₂. What is the oscillation angular frequency of the block if $k _ { 1 } = 7.6 \mathrm {~N} / \mathrm { m }$ and $k _ { 2 } = 5.0 \mathrm {~N} / \mathrm { m } ?$

A) 2.5 rad/s
B) 3.5 rad/s
C) 0.40 rad/s
D) 0.56 rad/s

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

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Question 52

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A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute?

A) 30,700
B) 8.53
C) 26.8
D) 1610
E) 512

F) A) and E)
G) A) and D)

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Question 53

Multiple Choice

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A 51.8-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 (force constant) of the bungee cord?

A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz. (a)What is the maximum speed of that point in SI units? (b)What is the maximum acceleration of the point in SI units?

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?

The period of a simple pendulum that is 1.00 m long on another planet is $1.66 \mathrm {~s}$ What is the acceleration due to gravity on this planet if the mass of the pendulum bob is 1.5 kg?

A Christmas ornament made from a thin hollow glass sphere hangs from a small hook at its surface. It is observed to oscillate with a frequency of 2.50 Hz in a city where g = 9.80 m/s². What is the radius of the ornament? The moment of inertia of a hollow sphere of mass M and radius R about a point on its edge is 5MR²/3.

A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s², what is true about the periods of these two systems?

If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?

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. What are the (a)maximum speed and (b)maximum acceleration of the tip of the needle?

The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm)cos[(5.46 s^-1)t]. Write an expression for the velocity of the particle as a function of time using the sine function.

A 0.50-kg object is attached to an ideal spring of spring constant (force 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. What are (a)the total energy and (b)the amplitude of vibration of the system?

The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm) cos[(6.35 s^-1) t]. At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm?

A 1.5-kg cart attached to an ideal spring with a force constant (spring constant)of 20 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium position. (a)What is the frequency of the oscillations of the cart? (b)Determine the maximum speed of the cart. Where does the maximum speed occur? (c)Find the maximum acceleration of the mass. Where does the maximum acceleration occur? (d)How much total energy does this oscillating system contain? (e)Express the displacement as a function of time using a cosine function.

A mass on a spring undergoes SHM. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.)

If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?

Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g = 1.6 m/s², and set into oscillation. Which of the following statements about these systems are true? (There could be more than one correct choice.)

A block attached to an ideal spring of force constant (spring constant) 15 N/m executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s² . The mass of the block is closest to

If both the mass of a simple pendulum and its length are doubled, the period will

If a pendulum makes 12 complete swings in 8.0 s, what are its (a)frequency and (b)period?