Find the Laplace transform for f(t)=2u(t-u)cos^2 2t-6e^(2t+7) delta(t+3)

Question

Find the Laplace transform for f(t)=2u(t-u)cos^2 2t-6e^(2t+7) delta(t+3)

midtlinjeg 2021-01-05 Answered

Find the Laplace transform for
$f (t) = 2 u (t - 3) \cos^{2} 2 t - 6 e^{2 t + 7} δ (t + 3)$

Ask Expert 1 See Answers

You can still ask an expert for help

Expert Answer

Benedict

Answered 2021-01-06 Author has 108 answers

Step 1
Calculate the Laplace transform:

\int_{- \infty}^{\infty} f (t) e^{- s t} d t = \int_{- \infty}^{\infty} (2 u (t - 3) \cos^{2} 2 t - 6 e^{2 t + 7} δ (t + 3)) e^{- s t} d t

= 2 \int_{- \infty}^{\infty} u (t - 3) \cos^{2} 2 t \cdot e^{- s t} d t - 6 \int_{- \infty}^{\infty} e^{2 t + 7} δ (t + 3) e^{- s t} d t

= 2 \int_{3}^{\infty} e^{- s t} \cos^{2} 2 t d t - 6 e^{3 s + 1}

= \int_{3}^{\infty} e^{- s t} (\cos 4 t + 1) d t - 6 e^{3 s + 1}

= \int_{3}^{\infty} e^{- s t} \cos 4 t d t + \int_{3}^{\infty} e^{- s t} d t - 6 e^{3 s + 1}

= \int_{3}^{\infty} e^{- s t} \cos 4 t d t + \frac{1 - e^{- 3 s}}{s} - 6 e^{3 s + 1}

= \int_{3}^{\infty} e^{- s t} \frac{e^{4 j t} + e^{- 4 j t}}{2} d t + \frac{1 - e^{- 3 s}}{s} - 6 e^{3 s + 1}

= \int_{3}^{\infty} \frac{e^{- s t + 4 j t} + e^{- s t - 4 j t}}{2} d t + \frac{1 - e^{- 3 s}}{s} - 6 e^{3 s + 1}

Not exactly what you’re looking for? Ask My Question This is helpful 40

Relevant Questions

asked 2021-02-04

A 17.8 kg flood light in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole. A cable connected to the beam helps to support the light. (In thefigure, $θ$ = 34.2 degrees. Find (A) The tension in the cable and (B) the horizontal and (C) vertical forces exerted on the beamby the pole.

(A) 320 N
(B) 250 N
(C) 0

See answers (1)

asked 2020-12-28

Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide down a 30.0 degree inclined plane. The coefficient of kinetic friction between the 4.00-kg block and the plane is 0.25; that between the 8.00-kg block and the plane is 0.35.
a) Calculate the acceleration of each block
b) Calculate the tension in the string
c) What happens if the positions of the block are reversed, so that the 4.00-kg block is above the 8.00-kg block?

See answers (2)

asked 2020-11-22

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive straight back toward the pitcher at 52.0 m/s. If the contact time between bat and ball is

1.00 \times 10^{- 3}

s,calculate the average force between the bat and ball during contest.

See answers (2)

asked 2020-10-26

A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm. What torque will bring the balls to a halt in 5.0 s? Answer in Nm.

See answers (1)

asked 2020-11-30

Find inverse laplace
find y(t) for the following
$Y (s) = \frac{8}{s} + \frac{1}{s - 3} \cdot e^{- 2 s}$

See answers (1)

asked 2021-10-30

Using the definition of continuity, explain why the beatiful piece-wise function $f (x) = {\begin{cases} \cos (x), & f o r x < 0 \\ 1, & f o r x = 0 \\ 1 - x^{2}, & f o r x > 0 \end{cases}$ is continuous at x=0. Show work to support your explanation.

See answers (1)

asked 2021-01-10

Prove that for $n \geq 2, 2 \cdot (\begin{matrix} n \\ 2 \end{matrix}) + (\begin{matrix} n \\ 1 \end{matrix}) = n^{2}$

See answers (1)

Secondary

Post Secondary