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A spring-mass-damper system has the following equilibrium equation: d²y dy +3+ 40y = 0 , t>0 dt² dt where y(t) = displacement in meters, and t = time in seconds. (3-a) Determine the general solution of y(t). (3-b) Assuming y(0) = 0 and y'(0) = 1, determine the particular solution of y(t). (3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (2-b). (3-d) Comment on how your mathematical solution behaves in transient and steady state regions. (3-e) Build a Simulink block model suitable for generating the results of the DE. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (3-f) Assuming that the right hand side of the given equilibrium equation is changed from 0 to 5, repeat parts (3-a,b,c,d, and e).

A spring-mass-damper system has the following equilibrium equation: d²y dy +3+ 40y = 0 , t>0 dt² dt where y(t) = displacement in meters, and t = time in seconds. (3-a) Determine the general solution of y(t). (3-b) Assuming y(0) = 0 and y'(0) = 1, determine the particular solution of y(t). (3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (2-b). (3-d) Comment on how your mathematical solution behaves in transient and steady state regions. (3-e) Build a Simulink block model suitable for generating the results of the DE. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (3-f) Assuming that the right hand side of the given equilibrium equation is changed from 0 to 5, repeat parts (3-a,b,c,d, and e).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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A spring-mass-damper system has the following equilibrium equation: d²y dy +3+ 40y = 0 , t>0 dt² dt where y(t) = displacement in meters, and t = time in seconds. (3-a) Determine the general solution of y(t). (3-b) Assuming y(0) = 0 and y'(0) = 1, determine the particular solution of y(t). (3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (2-b). (3-d) Comment on how your mathematical solution behaves in transient and steady state regions. (3-e) Build a Simulink block model suitable for generating the results of the DE. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (3-f) Assuming that the right hand side of the given equilibrium equation is changed from 0 to 5, repeat parts (3-a,b,c,d, and e).
Transcribed Image Text:A spring-mass-damper system has the following equilibrium equation: d²y dy +3+ 40y = 0 , t>0 dt² dt where y(t) = displacement in meters, and t = time in seconds. (3-a) Determine the general solution of y(t). (3-b) Assuming y(0) = 0 and y'(0) = 1, determine the particular solution of y(t). (3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (2-b). (3-d) Comment on how your mathematical solution behaves in transient and steady state regions. (3-e) Build a Simulink block model suitable for generating the results of the DE. Show the model and the results in your report and specify the transient and steady state regions. Make sure you submit the simulation file (properly named). (3-f) Assuming that the right hand side of the given equilibrium equation is changed from 0 to 5, repeat parts (3-a,b,c,d, and e).
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