1. (3 points each) Find the following functions, (a) _{(t - 1) step(t – 4)} (b)...
1. (3 points each) Find the following functions, (a) L{(t – 1) step(t – 4)} -4.5 (b) £'{S-2} } 2s + 1 (C) L-'{ s2 + 6s + 25
1. (3 points each) Find the following functions, (a) L{(t – 1)-step(t – 4)}
Find the Laplace transform of each of the following functions. 1. $(t) = f*(4(t – 1)* sin(67) dt L{v(t)}(s) = b. g(t) = [ e 2-3(t-1) cos(71) dT L{$(t)}(s) = c. y(t) = e5(t-1) sin(97) cos(6(t – T)) dt L{s(t)}(s) =
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 = eat sin(bt) 11, 0<t<1, (c) f3 = -1 1<t<2, | 2, t>2, Find the functions from their Laplace transforms: (a) Lyı] s(s + 1) (s +3) 2+s (b) L[42] = 52 + 2 s +5 (c) L[y3] = Solve the following initial value problems using the Laplace transform. Confirm each solution with a Matlab plot showing the function on the interval 0 <t<5. (a)...
help 1. (10 points) Find the inverse Laplace f(t) = --'{F} of the following: 4 6 1 a) 2 F(s) + S 8 +8 S b) 2 F(s) c) 2 F(8) (8 - 1)(8-2) 8 +3 $2 + 2s +5 7s2 + 23s + 30 (8-2)(82 +2s + 5) d) F(s)
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 (t) = + cos 3+ + 3e-24 2. 2 (t) = (1 - *) (Hint: expand...) 3. 2 (t) = tsin? t (Hint: use half angle formula first...) 4. 2 (t) = cos(36) - 1
Question 5. (8 points) Find the following: (a) L{t- sin(2t)} (b) C{2* * cos(t)} (c) c- )4+{2+2 +5} 4s S2 + 2s + 5 (d) C-1 6e-3 $2 +1
this is a differential equation question please solve them with steps and details also, make sure it is correct 1. (3 points each) Find the following functions, (a) C{(t - 1) step(t - 4)} (b) C-{ S-2 } 2s +1 (c) C-{ s2 + 6s + 25
Express f in terms of unit step functions. fo) 1- 3 t-(t-1)2(t-1)-T(t-4) O t2(t-4) O t-1+ (t-4) O ti(t-1) _ (t-1)- (t-4) Find f(t) and Xset f(t). (Enter your answer in terms of s.) Xiet f(t))