12.17 a. Find the Laplace transform of te at. b. Use the first derivative (time) operational transform given in Table 12.2C to find 1 the Laplace transform of (te-at).

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12.17
a. Find the Laplace transform of te-at.
b. Use the first derivative (time) operational transform given in Table 12.2 to find
1 the Laplace transform of (te-at).
Transcribed Image Text:12.17 a. Find the Laplace transform of te-at. b. Use the first derivative (time) operational transform given in Table 12.2 to find 1 the Laplace transform of (te-at).
LTE+
6:49
TABLE 12.2 An Abbreviated List of Operational Transforms
Operation
F(s)
Multiplication by a constant
Kf()
KF(s)
Addition/subtraction
fi) + f) - fs() + ...
F(s) + F(s) - F(s) + ..
af()
First derivative (time)
sF(s) – f(0)
di
d²f)
di?
df (0)
s*F(s) – sf(0") -
di
Second derivative (time)
d"f(t)
s"F(s) – s*-lf(0") – s"-24f(0)
dt
nth derivative (time)
dt"
di?
F(s)
Time integral
Translation in time
f( - a)u(t - a), a > 0
e"F(s)
Translation in frequency
F(s + a)
Scale changing
f(at), a >0
dF(s)
First derivative (s)
if(1)
II
ds
d"F(s)
(-1)-
ds"
nth derivative (s)
"f()
s integral
| F(u)du
Transcribed Image Text:LTE+ 6:49 TABLE 12.2 An Abbreviated List of Operational Transforms Operation F(s) Multiplication by a constant Kf() KF(s) Addition/subtraction fi) + f) - fs() + ... F(s) + F(s) - F(s) + .. af() First derivative (time) sF(s) – f(0) di d²f) di? df (0) s*F(s) – sf(0") - di Second derivative (time) d"f(t) s"F(s) – s*-lf(0") – s"-24f(0) dt nth derivative (time) dt" di? F(s) Time integral Translation in time f( - a)u(t - a), a > 0 e"F(s) Translation in frequency F(s + a) Scale changing f(at), a >0 dF(s) First derivative (s) if(1) II ds d"F(s) (-1)- ds" nth derivative (s) "f() s integral | F(u)du
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