Explicitly calculate the Laplace transforms of the following functions. Also state the region where it is...
Calculate the Laplace transform of the following time functions
by applying the Laplace transform properties:
f) f(t) = 3t cos(t) g) f(t) = 3t sin(3t) h) f(t) = 2te*** – 3t sin(t) i) f(t) = t sin(3t) + 2t cos(t) j) f(t) = 5sin(t)/(3t)
2. Find the Laplace transform of the following functions (a) f(t)3t+4 (b) cos(2Tt) (c) sin(2t T) (d) sin(t) cos(t) "Use Trig. Identity" (e) f(t) te 2t use first shifting theorem
Hollie work #2 (Due April 1 δ) Problem Obtain the Laplace transform of each of the following functions: 2t (a) et cos 3tu(t) (c) e3 cosh 2tu(t) (e) te sin 2tu(t) (b) e2t sin 4tu(t) (d) e4 sinh tu(t) Problem 2. Find the Laplace transform of each of the following functions (b) 3f* e^ut) (c) 2n1(t)-4". δ(t) (e) 5u(t/2) (d) 2e) u(t) 2p-(t-1) (f) 6el3 u(t) d" dt" Problem 3. Find the Laplace transform of the following signals (a) f(t)-(2t...
dan Multiplication by t. 8. Find the following Laplace transforms using the formula L[t"f(t)] = (-1)", (a) [t3e-36] (b) C[(t + 2)2e'] (c) C[t(3 sin 2t - 2 cos 2t)] (d) L[tsin t] (e) C[t cosh 3t) (1) [(t-1)(t - 2) sin 3t] (g) [t3 cost] 9. Applying L[t"f(t)] = (-1)", , calculate (a) Sºte-3t sin t dt (b) Scºt?e-t cost dt recimento e contato Llegarsim 225 (-1)" IEC d'Fs) dsh
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms of the given functions. (s > 0) 1 (s > 0) S- 1. Kt) = 12 2. f = 23t+1 Use transforms from the Table (op right) to find the Laplace transforms of the given functions. t" ( n20) (s > 0) r(a + 1) 1a (a > -1) (s > 0) 5+1 3. f(t) = VE +8t 4. f(t) = sin(2tcos(2t) Use the...
4. Find the LaPlace transforms for the following functions. (5pts) (a) f(t) = 3t2 - sin 3t (b) t +1 (2-et ostsil t21
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)...
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(1 point) Find the Laplace Transform of the following functions: f(t) = 2e-9t + 7++ 4t+3 F(s) = f(t) = 2e9t sin(7t) + 4ť + 3et F(s) = -9t f(t) = 2te-94 sin(7t) F(s) = Note that there is a table of Laplace transforms in Appendix C, page 1271 thru 1273 of the book.
Find the Laplace transforms of the following functions:
a) f(t) = sin(at + b) Using the integral of the
Laplace transform
b) f(t) = cos(t) + sin(t/2) You can directly use
table 5.1
Tableau 5.1 Transformées de Laplace les plus couramment utilisées f(t)= £. {F()} F(s)= £{f(t)} f(t)=1 F(s) = 2 f(t)=1 F(s) == 2 3 Sl)=12 F(s) n! 4 St=1" F(s)=- 5 () at F(s)- S-a n! 6 S()=1"ar F($)= (s-a)"+1 a 7 s(t)= sin(at) F(s) s? +a? S...
1) Laplace transforms/Transfer functions Use Laplace transform tables!!!! 1.1: Find the Laplace transform of f(t) = (cos(2t) + e-4t)-u(t) (simplify into one ratio)