A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 9 inches below the equilibrium position. (a) Find the position x of the mass at the times t = 1/12, 1/8, n/6, 1/4, and 9n/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(n/12) = ft Χ(π/8) - ft x(π/6) - ft Χ (π/4 ) - ft x(9n/32) = ft (b) What is the velocity of the mass when t = 3n/16 s? ft/s In which direction is the mass heading at this instant? O downward O 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 9 inches below the equilibrium position. (a) Find the position x of the mass at the times t = 1/12, 1/8, n/6, 1/4, and 9n/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.) x(n/12) = ft Χ(π/8) - ft x(π/6) - ft Χ (π/4 ) - ft x(9n/32) = ft (b) What is the velocity of the mass when t = 3n/16 s? ft/s In which direction is the mass heading at this instant? O downward O upward (c) At what times does the mass pass through the equilibrium position? , n = 0, 1, 2, ...
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
Related questions
Question
Transcribed Image Text:A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 9 inches below the equilibrium position.
(a) Find the position x of the mass at the times t = t/12, t/8, 1/6, 1/4, and 9n/32 s. (Use g = 32 ft/s² for the acceleration due to gravity.)
Χ (π/12)
ft
%3D
Χ (π/8) -
ft
x(T/6) =
ft
Χ (π/4) -
ft
x(9п/32) %3
ft
(b) What is the velocity of the mass when t = 31/16 s?
ft/s
In which direction is the mass heading at this instant?
O downward
O upward
(c) At what times does the mass pass through the equilibrium position?
, п %3D 0, 1, 2, ...
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning