Write the corresponding differential equation in time domain. F(s) X(s) s³ + 11s² + 12s + 18 s+3 d²x(t) dt2 d²f(t) 3df(t) d³x(t) dt3 dx(t) + 18x(t) : dt + 11- + 12 dt dt d³x(t) + 11 dx(t) d?x(t) + 12 dt² dt d²f(t) _ 3f(t) + 18x(t) dt3 dt d³x(t) dt3 d²x(t) + 11 + 12 dt² dx(t) + 18x(t): dt df(t) - 3f (t) dt d³x(t) dt3 d?x(t) + 11 dt? dx(t) + 12 + 18x(t) dt df (t) + 3f(t) dt
Write the corresponding differential equation in time domain. F(s) X(s) s³ + 11s² + 12s + 18 s+3 d²x(t) dt2 d²f(t) 3df(t) d³x(t) dt3 dx(t) + 18x(t) : dt + 11- + 12 dt dt d³x(t) + 11 dx(t) d?x(t) + 12 dt² dt d²f(t) _ 3f(t) + 18x(t) dt3 dt d³x(t) dt3 d²x(t) + 11 + 12 dt² dx(t) + 18x(t): dt df(t) - 3f (t) dt d³x(t) dt3 d?x(t) + 11 dt? dx(t) + 12 + 18x(t) dt df (t) + 3f(t) dt
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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This is a Laplace Transform question, solve for the corresponding differential equation.
![Write the corresponding differential equation in time domain.
F(s)
X(s) s³ + 11s² + 12s + 18
s+3
d³x(t)
dt3
d²x(t)
dt2
d²f(t) 3df(t)
dx(t)
+ 18x(t) :
dt
+ 11-
+ 12
dt
dt
d³x(t)
+ 11
dx(t)
d?x(t)
+ 12
dt²
dt
d²f(t) _ 3f(t)
+ 18x(t)
dt3
dt
d³x(t)
dt3
d²x(t)
+ 11
+ 12
dt²
dx(t)
+ 18x(t):
dt
df(t)
– 3f(t)
dt
d³x(t)
dt3
d?x(t)
+ 11
dt?
dx(t)
+ 12
+ 18x(t)
dt
df (t)
+ 3f(t)
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F099318eb-d94e-4371-9177-5fd1fd819e1d%2F4d59611c-600e-48b2-902f-bb1e5263a7f6%2Fbc4lizl_processed.png&w=3840&q=75)
Transcribed Image Text:Write the corresponding differential equation in time domain.
F(s)
X(s) s³ + 11s² + 12s + 18
s+3
d³x(t)
dt3
d²x(t)
dt2
d²f(t) 3df(t)
dx(t)
+ 18x(t) :
dt
+ 11-
+ 12
dt
dt
d³x(t)
+ 11
dx(t)
d?x(t)
+ 12
dt²
dt
d²f(t) _ 3f(t)
+ 18x(t)
dt3
dt
d³x(t)
dt3
d²x(t)
+ 11
+ 12
dt²
dx(t)
+ 18x(t):
dt
df(t)
– 3f(t)
dt
d³x(t)
dt3
d?x(t)
+ 11
dt?
dx(t)
+ 12
+ 18x(t)
dt
df (t)
+ 3f(t)
dt
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