Question

In: Advanced Math

Find the Laplace Transform of the functions t , 0 ≤ t < 1 (a) f(x)...

Find the Laplace Transform of the functions

t , 0 ≤ t < 1

(a) f(x) =     2 − t , 1 ≤ t < 2

0 , t ≥ 2

(b) f(t) = 12 + 2 cos(5t) + t cos(5t)

(c) f(t) = t 2 e 2t + t 2 sin(2t)

Solutions

Expert Solution


Related Solutions

Find the Laplace transform of the following functions. (a)  f (t)  =  { 6 0  < ...
Find the Laplace transform of the following functions. (a)  f (t)  =  { 6 0  <  t  ≤  4 8 t  ≥  4 (b)  f (t)  =  { t2 0  ≤  t  <  3 0 t  ≥  3 (c)  f (t)  =  { 0 0  ≤  t  <  π/4 cos[7(t − π/4)] t  ≥  π/4
1. Find the Laplace transform of each of the following functions: (a). f(t) = t ,...
1. Find the Laplace transform of each of the following functions: (a). f(t) = t , (b). f(t) = t2  , (c) f(t) = tn  where n is a positive integer Laplace transform of the given function 2. . f(t) = sin bt 3.   f(t) = eat sin bt
Find the laplace transform of the following functions, using the definition of Laplace transforms: f(t)=-2cos4t f(t)=2...
Find the laplace transform of the following functions, using the definition of Laplace transforms: f(t)=-2cos4t f(t)=2 sin^2(t) g(t)=3e^tcos(t)
. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t)...
. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t) = 5e^3t cos(4t) − 6e^2t sin(7t)
1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)=...
1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)= 3) Find the Laplace transform of f(t)=u(t−6)⋅t^2 F(s)=
Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t)    f(0)=0 f'(0)=0    f''(0)=0...
Solve the following IVP specifically using the Laplace transform method (d^3)x/d(t^3)+x=e^(-t)u(t)    f(0)=0 f'(0)=0    f''(0)=0 where u(t) is the Heaviside step function
Find Laplace transform of 50x''+ 100x' + 60x = 0, x'(0)=0, x(0)=0
Find Laplace transform of 50x''+ 100x' + 60x = 0, x'(0)=0, x(0)=0
Take the Laplace transform of the following initial value and solve for X(s)=L{x(t)}X(s)=L{x(t)}: x′′+16x={sin(πt),0} 0≤t<1 1≤t...
Take the Laplace transform of the following initial value and solve for X(s)=L{x(t)}X(s)=L{x(t)}: x′′+16x={sin(πt),0} 0≤t<1 1≤t x(0)=0 x′(0)=0. a) X(s)=   Now find the inverse transform to find b) x(t)= Use u(t−a) for the Heaviside function shifted a units horizontaly.
Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and...
Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and f(1) = 1.
Solve with Laplace transform 1. y''+ 4 t y'− 4y = 0, y(0) = 0, y'(0)...
Solve with Laplace transform 1. y''+ 4 t y'− 4y = 0, y(0) = 0, y'(0) = −7 2. (1− t) y''+ t y' − y = 0, y(0) = 3, y'(0) = −1
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT