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The motion of a damped spring-mass system as give is described by the following ordinary differential equation: m d²x dx + c dt2 dt + kx = 7 where x = displacement from equilibrium position (m), t =time in second, m =10 kg mass and c = the damping coefficient (N s/m). The damping coefficient c take on the value of 200 (overdamped) and the spring constant k = 15 N/m. The initial velocity is zero and the initial displacement x = 3 m. Find the displacement r(t) using Laplace transforms method. Then, calculate x(t) for t= 5, 10, 15 seconds. (a)

The motion of a damped spring-mass system as give is described by the following ordinary differential equation: m d²x dx + c dt2 dt + kx = 7 where x = displacement from equilibrium position (m), t =time in second, m =10 kg mass and c = the damping coefficient (N s/m). The damping coefficient c take on the value of 200 (overdamped) and the spring constant k = 15 N/m. The initial velocity is zero and the initial displacement x = 3 m. Find the displacement r(t) using Laplace transforms method. Then, calculate x(t) for t= 5, 10, 15 seconds. (a)

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
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1. The motion of a damped spring-mass system as give is described by the following ordinary differential equation: m d²x dx +c dt² dt + kx = 7 where x = displacement from equilibrium position (m), t=time in second, m =10 kg mass and c = the damping coefficient (N s/m). The damping coefficient c take on the value of 200 (overdamped) and the spring constant k = 15 N/m. The initial velocity is zero and the initial displacement x = 3 m. Find the displacement x(t) using Laplace transforms method. Then, calculate x(t) for t= 5, 10, 15 seconds. (a)
Transcribed Image Text:1. The motion of a damped spring-mass system as give is described by the following ordinary differential equation: m d²x dx +c dt² dt + kx = 7 where x = displacement from equilibrium position (m), t=time in second, m =10 kg mass and c = the damping coefficient (N s/m). The damping coefficient c take on the value of 200 (overdamped) and the spring constant k = 15 N/m. The initial velocity is zero and the initial displacement x = 3 m. Find the displacement x(t) using Laplace transforms method. Then, calculate x(t) for t= 5, 10, 15 seconds. (a)
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