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(3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (2-b).

(3-c) Use Laplace transform to solve the given differential equation with the same initial conditions in (2-b).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part c please

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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