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If the mass is set in motion from its position function at any give-

If the mass is set in motion from its position function at any give-

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb-sec/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 3 in/sec, find its position function at any given time. Let t = time in seconds Let y = position in feet Integers, rational or square root values, i.e. no decimals throughout the problem for credit. a) Determine the mass. b) Determine the force function from Hooke's Law. c) Determine the damping force function. d) Determine the differential equation with the exact constants given. e) Determine the initial values. f) Solve the differential equation with the exact constants to prove. Hint: balance the ODE to remove all rational constants. Solving a formulized ODE then plugging in the constants at the end will not be given credit.
Transcribed Image Text:A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a damping constant of 2 lb-sec/ft. If the mass is set in motion from its equilibrium position with a downward velocity of 3 in/sec, find its position function at any given time. Let t = time in seconds Let y = position in feet Integers, rational or square root values, i.e. no decimals throughout the problem for credit. a) Determine the mass. b) Determine the force function from Hooke's Law. c) Determine the damping force function. d) Determine the differential equation with the exact constants given. e) Determine the initial values. f) Solve the differential equation with the exact constants to prove. Hint: balance the ODE to remove all rational constants. Solving a formulized ODE then plugging in the constants at the end will not be given credit.
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