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1) Find the Laplace transforms of the following functions. Use the Table of Laplace Transforms in your textbook. a) $f_1(t) = t^3e^{-2t}cos(2t)$ b) $f_2(t) = cos(t-T).1(t-T)$ c) $f_3(t) = cos(t).1(t-T)$ d) $f_4(t) = cos(t-T).1(t)$ 2) Solve the ODE using Laplace transformation a) $\ddot{x}(t) + 5\dot{x}(t) + 4x(t) = e^{-2t}$, $x(0) = \dot{x}(0) = 1$ b) $\ddot{x} + 2x = \delta(t)$, $x(0^-) = 0$ c) $\ddot{y}(t) + 2\dot{y}(t) + 2y(t) = 0; y(0) = 0, \dot{y}(0) = 1$ d) $\ddot{y}(t) - 2\dot{y}(t) + 2y(t) = 0; y(0) = 2, \dot{y}(0) = 2$

          1) Find the Laplace transforms of the following functions. Use the Table of Laplace
Transforms in your textbook.
a) $f_1(t) = t^3e^{-2t}cos(2t)$
b) $f_2(t) = cos(t-T).1(t-T)$
c) $f_3(t) = cos(t).1(t-T)$
d) $f_4(t) = cos(t-T).1(t)$
2) Solve the ODE using Laplace transformation
a) $\ddot{x}(t) + 5\dot{x}(t) + 4x(t) = e^{-2t}$,  $x(0) = \dot{x}(0) = 1$
b) $\ddot{x} + 2x = \delta(t)$, $x(0^-) = 0$
c) $\ddot{y}(t) + 2\dot{y}(t) + 2y(t) = 0; y(0) = 0, \dot{y}(0) = 1$
d) $\ddot{y}(t) - 2\dot{y}(t) + 2y(t) = 0; y(0) = 2, \dot{y}(0) = 2$

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1) Find the Laplace transforms of the following functions. Use the Table of Laplace
Transforms in your textbook.
a) f1(t) = t^3e^-2tcos(2t)
b) f2(t) = cos(t-T).1(t-T)
c) f3(t) = cos(t).1(t-T)
d) f4(t) = cos(t-T).1(t)
2) Solve the ODE using Laplace transformation
a) ẍ(t) + 5ẋ(t) + 4x(t) = e^-2t, x(0) = ẋ(0) = 1
b) ẍ + 2x = δ(t), x(0^-) = 0
c) ÿ(t) + 2ẏ(t) + 2y(t) = 0; y(0) = 0, ẏ(0) = 1
d) ÿ(t) - 2ẏ(t) + 2y(t) = 0; y(0) = 2, ẏ(0) = 2

Added by Julie S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shaiju T

06/13/2022

Step 1

Therefore, the Laplace transform of t^3e^(-2t)cos(2t) can be found by taking the Laplace transform of each component separately: L{t^3} = 3!/s^4 = 6/s^4 L{e^(-2t)} = 1/(s+2) = 1/(s+2) L{cos(2t)} = s/(s^2+2^2) = s/(s^2+4) So, the Laplace transform of fi(t) Show more…

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Plase do the math for each question l Find the Laplace transforms of the following functions. Use the Table of Laplace Transforms in your textbook. a) fi(t)=t3e-2t cos(2t) b) f(t)=cos(t-T)1(t-T) c) f(t)=cos(t).1(t-T) d) f4(t)=cos(t-T)1(t) 2) Solve the ODE using Laplace transformation x(t)+5x(t)+4x(t) =e-2t x(0)=x(0)=1 b) x+2x=6(t), x(0)=0 c)y(t)+2y(t)+2y(t)=0;y(0)=0,y(0)=1 d)y(t)-2y(t)+2y(t)=0;y(0)=2,y(0)=2

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