Question

Find the Laplace Transform of the following functions:

1. e^(-2t+1)

2. cos^2(2t)

3. sin^2(3t)

Answer #1

Compute the Laplace transform of functions
a) f(t) = e^(−3t) sin(5t)
b) f(t) = (2t + 3)e^(−t)

Derive the Laplace transform of the following time domain
functions
A) 12 B) 3t sin(5t) u(t) C) 2t^2 cos(3t) u(t) D) 2e^-5t
sin(5t)
E) 8e^-3t cos(4t) F) (cost)&(t-pi/4)

Find the Laplace transform for the following functions. Show all
work.
(a) u(t-1) - u(t-2)
(b) sin(2t-4)u(t-2)

Derive the Laplace transform for the following time
functions:
a. sin ωt u(t)
b. cos ωt u(t)

determine the Laplace transform of the following functions:
a) f(t) = { 1 if 0 < t < 5,
0 if 5 < t < 10,
e^ 4t if t > 10
b) g(t) = 6e −3t − t 2 + 2t − 8

a) Find the Laplace Transform of : (?) ???3? cos 2? (??) ? −2?
???2 ?
b) Find the Inverse Laplace Transform of: (?) ?−4 /
?2−4 (??) 4 / s2−2?−3

a.) Find the Laplace transform of ?(?)=1+?(?−5)⋅(?+9)
b.) Find the Laplace transform of?(?)=?(?−4)⋅?^2
c.) Find the Laplace transform of?(?)=?(?−(3?)/2)⋅sin(?)
d.) Find the Laplace transform of ?(?)=?(?−4)⋅?^(−?)

laplace transform
y''+y = cos(2t) y(0) =1 y'(0) = -4

Find the laplace transform of sin root t and hence deduce cos
root t all over root t

Differential Geometry
(6) Find the Frenet apparatus of α(t) = (e2t cos(2t),
e2t sin(3t), e2t ).

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