Find the initial value for the function f\{t\}=2u(t)+3\cos u(t)

sanuluy

sanuluy

Answered question

2021-09-15

Find the initial value for the function f{t}=2u(t)+3cosu(t)
a) 2
b) 3
c) 5
d) 4

Answer & Explanation

funblogC

funblogC

Skilled2021-09-16Added 91 answers

Step 1
Consider the function f(t)=2u(t)+3cosu(t)
To find the initial value of this function, use the Laplace Initial Value Theorem.
Take the Laplace transform of the given function to get
L{f(t)}=L{2u(t)+3cosu(t)}
F(s)=2L{u(t)}+3L{cosu(t)}
F(s)=21s+3ss2+1
F(s)=2s+3ss2+1
sF(s)=2+3s2s2+1
sF(s)=2+31+1s2
Step 2
Now, by the Laplace initial value theorem, we know that
limt0+f(t)=limssF(s)=f(0+)
So, using this we have
limssF(s)=lims[2+31+1s2]
=2+31+1
=2+31+0
=2+31
=2+3
=5
=f(0+)
Thus, the initial value of the given function is c) 5.

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