Express the inverse Laplace transform of the function shown to the right via the completing-the-square method: Evaluate the discriminant of the quadratic factor in the denominator to confirm that its roots are complex. b. 5s +45 X(s) = (s? +4s+13)(s+1) a. Complete the square for the first two terms of the quadratic factor; this indicates a frequency shift or time-domain multiplication by a decaying exponential. Determine critical frequency after accounting for frequency shift. d. c. Express/solve partial fraction expansion. Express time-domain functions. e.

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Express the inverse Laplace transform of the function shown to the right via
the completing-the-square method:
Evaluate the discriminant of the quadratic factor in the denominator
to confirm that its roots are complex.
b.
5s +45
X(s) =
(s? +4s+13)(s+1)
a.
Complete the square for the first two terms of the quadratic factor;
this indicates a frequency shift or time-domain multiplication by a
decaying exponential.
Determine critical frequency after accounting for frequency shift.
d.
c.
Express/solve partial fraction expansion.
Express time-domain functions.
e.
Transcribed Image Text:Express the inverse Laplace transform of the function shown to the right via the completing-the-square method: Evaluate the discriminant of the quadratic factor in the denominator to confirm that its roots are complex. b. 5s +45 X(s) = (s? +4s+13)(s+1) a. Complete the square for the first two terms of the quadratic factor; this indicates a frequency shift or time-domain multiplication by a decaying exponential. Determine critical frequency after accounting for frequency shift. d. c. Express/solve partial fraction expansion. Express time-domain functions. e.
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