L-`1{1/s+a}=e-at , L-`1{1/(s+a)2}=te-at
answer
#6.) Given f(t)=-2:+8, Ost<4, f(t+4)= f(t). Find F(s)=L{f(t)} of the Periodic Function.
9s 11 (1 pt) Find the inverse Laplace transform f(t) = L=1 {F(s)}| of the function F(s) s2 2s5 9s 11 f(t)= L' help (formulas) $2-2S+5
dn 6. Use the theorem, L {t" f(t)} = (-1)" den! F(s), to find each of the following: (a) L {t cos 2t} (b) L {t sint}
2. Use the property f(t) = L-1 {r(s))-(-1)"L-1 {F(n)(s)} (-t)n and choose n = 1 to perform the following inverse Laplace transform L-1 (F(s)): (1). F(s)=ln-s-3 V s + 1 (Answer:- (e3t-le-t) ) (2). F(s) - arctan(2s) (Answer: tsin ) 2. Use the property f(t) = L-1 {r(s))-(-1)"L-1 {F(n)(s)} (-t)n and choose n = 1 to perform the following inverse Laplace transform L-1 (F(s)): (1). F(s)=ln-s-3 V s + 1 (Answer:- (e3t-le-t) ) (2). F(s) - arctan(2s) (Answer: tsin )
Find the Inverse Transform L {F(s)} of F(s) 38+2 $2 -38 +2 o L 1{F(s)} = 8e2t - 5et OL-'{F(s)} 5 8-1 $ 2 L'{F(s)} = -5e2-8et None of them
(1 point) Find the inverse Laplace transform f(t) = L-i {F(s)) of the function F(s) = 52-9 help (formulas) s+3 s-3
f(t) = [5+ (4e2+ + 6te-2)e-24]u(t) A Find F(S) = L[f(t) as a proper rational function. F(s) must be in fully factored form.
Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (2t - 1)3 %3D L{f(t)} =
7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1) 7. (10) a) Find F(s) 1) if f) -tet [u(t)-u(t-4)] 2) iffit) d/dt [t sin (at )] u(t) (15) b) Find f(t) 1) if F(s)-10 s/[(s+1)(s+5)] 2) İfF(s) 10 (s+3)/[s2 (s+2)] 3) if F(s) - 10/(s2+s+ 1)
Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 5t? – 2 sin(3t) gif(t)} =