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A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = r/12, n/8, 1/6, x/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(7/12) = 0.666 X ft x(x/8) = 0.666 X ft x(x/6) = 0.665 X ft x(x/4) = 0.663 X ft x(9x/32) = 0.662 X ft (b) What is the velocity of the mass whent = 37/16 s? 16 3 ft/s In which direction is the mass heading at this instant? upward o downward (c) At what times does the mass pass through the equilibrium position? + 16 X , n = 0, 1, 2, ...

A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = r/12, n/8, 1/6, x/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(7/12) = 0.666 X ft x(x/8) = 0.666 X ft x(x/6) = 0.665 X ft x(x/4) = 0.663 X ft x(9x/32) = 0.662 X ft (b) What is the velocity of the mass whent = 37/16 s? 16 3 ft/s In which direction is the mass heading at this instant? upward o downward (c) At what times does the mass pass through the equilibrium position? + 16 X , n = 0, 1, 2, ...

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter12: Oscillatory Motion
Section: Chapter Questions
Problem 14P: In an engine, a piston oscillates with simple harmonic motion so that its position varies according...
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A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = 1/12, x/8, n/6, n/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(1/12) = 0.666 X ft X(x/8) = 0.666 X ft x(x/6) = 0.665 X ft x (π/4) 0.663 X ft = x(9л/32) 0.662 X ft (b) What is the velocity of the mass when t = 3x/16 s? 16 ft/s 3 In which direction is the mass heading at this instant? upward downward (c) At what times does the mass pass through the equilibrium position? 16 4 X , n = 0, 1, 2, .
Transcribed Image Text:A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = 1/12, x/8, n/6, n/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(1/12) = 0.666 X ft X(x/8) = 0.666 X ft x(x/6) = 0.665 X ft x (π/4) 0.663 X ft = x(9л/32) 0.662 X ft (b) What is the velocity of the mass when t = 3x/16 s? 16 ft/s 3 In which direction is the mass heading at this instant? upward downward (c) At what times does the mass pass through the equilibrium position? 16 4 X , n = 0, 1, 2, .
A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = n/12, n/8, n/6, a/4, and 97/32 s. (Use g = 32 ft/s? for the acceleration due to gravity.) X(1/12) = -0.33 X ft x(x/8) = -0.66 X ft x(л/6) %3 -0.33 X ft x(T/4) = 0.66 X ft x(9x/32) = 0.47 X ft (b) What is the velocity of the mass when t = 37/16 s? 16 ft/s 3 In which direction is the mass heading at this instant? upward downward (c) At what times does the mass pass through the equilibrium position? 16 4 X , n = 0, 1, 2, +
Transcribed Image Text:A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = n/12, n/8, n/6, a/4, and 97/32 s. (Use g = 32 ft/s? for the acceleration due to gravity.) X(1/12) = -0.33 X ft x(x/8) = -0.66 X ft x(л/6) %3 -0.33 X ft x(T/4) = 0.66 X ft x(9x/32) = 0.47 X ft (b) What is the velocity of the mass when t = 37/16 s? 16 ft/s 3 In which direction is the mass heading at this instant? upward downward (c) At what times does the mass pass through the equilibrium position? 16 4 X , n = 0, 1, 2, +
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