Question 2. Determine if the finger print method can be used to back transform each of the equations. Back transform the equation using this method if possible. If it is not possible explain why (briefly).
a)
No repeating s terms in the denominator and higher power of s in denominator thus the fingerprint method should work.
For the equation as written (s could be cancelled from top and bottom to make it easier) there are two roots, 0, and -a
Covering up s in the denominator gives:
Covering up s+a in the denominator gives:
Thus:
In this case the power of s in the denominator is the same as in the numerator so the fingerprint method cannot be used.
No repeating s terms in the denominator and higher power of s in denominator thus the fingerprint method should work.
For this equation there are three roots, 0, -a, and -b
Covering up s in the denominator gives:
Covering up s+a in the denominator gives:
Covering up s+b in the denominator gives:
Thus:
In this case there are repeating terms (s+a) in the denominator so the fingerprint method cannot be used.
No repeating s terms in the denominator and higher power of s in denominator thus the fingerprint method should work.
For this equation there are two roots, -a, and -b
Covering up s+a in the denominator gives:
Covering up s+b in the denominator gives:
Thus:
