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A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 3 inches below the equilibrium position. (a) Find the position x of the mass at the times t = π/12, π/8, π/6, π/4, and 9/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.) X(π/12) = -0.125 X(π/8)= -0.25 X(π/6)= -0.125 X(π/4) = 0.25 x(9π/32) = 1 4√2 ft ft ft (b) What is the velocity of the mass when t = 3π/16 s? ft/s In which direction is the mass heading at this instant? O downward upward (c) At what times does the mass pass through the equilibrium position? , n = 0, 1, 2, ...

A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 3 inches below the equilibrium position. (a) Find the position x of the mass at the times t = π/12, π/8, π/6, π/4, and 9/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.) X(π/12) = -0.125 X(π/8)= -0.25 X(π/6)= -0.125 X(π/4) = 0.25 x(9π/32) = 1 4√2 ft ft ft (b) What is the velocity of the mass when t = 3π/16 s? ft/s In which direction is the mass heading at this instant? O downward upward (c) At what times does the mass pass through the equilibrium position? , n = 0, 1, 2, ...

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 3 inches below the equilibrium position. (a) Find the position x of the mass at the times t = π/12, π/8, π/6, π/4, and 9/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.) X(π/12) = -0.125 X(π/8)= -0.25 X(π/6)= -0.125 X(π/4) = 0.25 x(9π/32) = 1 4√2 ft ft ft (b) What is the velocity of the mass when t = 3π/16 s? ft/s In which direction is the mass heading at this instant? O downward upward (c) At what times does the mass pass through the equilibrium position? , 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 3 inches below the equilibrium position. (a) Find the position x of the mass at the times t = π/12, π/8, π/6, π/4, and 9/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.) X(π/12) = -0.125 X(π/8)= -0.25 X(π/6)= -0.125 X(π/4) = 0.25 x(9π/32) = 1 4√2 ft ft ft (b) What is the velocity of the mass when t = 3π/16 s? ft/s In which direction is the mass heading at this instant? O downward upward (c) At what times does the mass pass through the equilibrium position? , n = 0, 1, 2, ...
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