Activity 3: A spring-mass-damper system has the following equilibrium equation: 4 d²y dy +3 +40y = 0, t> 0 dt dt² 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
Activity 3: A spring-mass-damper system has the following equilibrium equation: 4 d²y dy +3 +40y = 0, t> 0 dt dt² 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
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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3a 3b annd 3c please. In 3c its 3b not 2b.
Transcribed Image Text:Activity 3:
A spring-mass-damper system has the following equilibrium equation:
d?y
dy
4
+ 3
dt?
dt
+ 40y = 0 ,
t > 0
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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