A mass weighing 8 lbs stretches a spring 8 inches. The mass is pushed upwards, contracting the spring a distance of 2 inch and then set in motion with a downward velocity of 4 ft/sec. The mass is attached to a viscous damper that exerts a force of 6 pounds when the velocity of the mass is 3 ft/s. Use g 32 ft/sec2. a) Determine the mass m, spring coefficient K, and the damping coefficient y. b) Write an initial value problem to model the system and solve your IVP to find the position function u(t), for any time t. Write your final answer as a single term.
A mass weighing 8 lbs stretches a spring 8 inches. The mass is pushed upwards, contracting the spring a distance of 2 inch and then set in motion with a downward velocity of 4 ft/sec. The mass is attached to a viscous damper that exerts a force of 6 pounds when the velocity of the mass is 3 ft/s. Use g 32 ft/sec2. a) Determine the mass m, spring coefficient K, and the damping coefficient y. b) Write an initial value problem to model the system and solve your IVP to find the position function u(t), for any time t. Write your final answer as a single term.
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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Transcribed Image Text:A mass weighing 8 lbs stretches a spring 8 inches. The mass is pushed upwards, contracting the
spring a distance of 2 inch and then set in motion with a downward velocity of 4 ft/sec. The
mass is attached to a viscous damper that exerts a force of 6 pounds when the velocity of the
mass is 3 ft/s. Use g = 32 ft/sec.
a) Determine the mass m, spring coefficient K, and the damping coefficient y.
b) Write an initial value problem to model the system and solve your IVP to find the
position function u(t), for any time t. Write your final answer as a single term.
c) Determine the quasi-frequency u, period T4, phase shift 8, and amplitude R of the
vibration.
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