Question: Use the Final Value Theorem to predict y() BEFORE taking the inverse Laplace. Also check y(0) using the Initial Value Theorem. The differential equation

Use the Final Value Theorem to predict y() BEFORE taking the inverse Laplace. Also check y(0) using the Initial Value Theorem. The differential equation da +6y +9y=cost dt has initial conditions, y(0) = 1, y' (0) = 2. If y(s) = s+1 s(s+45+8) find y(t).

Step by Step Solution

★★★★★

3.42 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Use the final value theorem to determinethe final value for f(t) below: (a) Ps = 3x+1 58(x-2)

Prove the final value theorem for the one-sided z-transform.

Find The Inverse Laplace Transform Of S26s 7s34s2 5s 2 Find The Inverse Laplace Transform Of E2ss2(s1) This problem has been solved

In the following problems we use the inverse Laplace transform and the relation between input and output of LTI systems. (a) The Laplace transform of the output of a system is find y 1 (t), assume it...

1130 The step response of a linear circuit is g t =0:5 1 e250 t u t . Find the output waveform when the input is v1t = 20 e200t u t . Use MATLAB to find the Laplace transforms of gt and v1t....

NOTE: WRITE THE ANSWERS CLEARLY AND UNDERSTANDABLE TO SEE BECAUSE I AM HAVING A HARD TIME SEEING MESSY HANDWRITING *SHOW THE COMPLETE SOLUTION 1. Consider the 2'\"1 order differential equation 2 d f...

Find the inverse Laplace transform $\mathscr{L}^{-1}\left\{\frac{e^{-\pi s} s}{\left(s^{2}+1ight)}ight\}$ using the second shifting theorem, and sketch the resultant function.

The step response of a linear circuit is $g(t)=0.5$ [1$\left.e^{-250 t}ight] u(t)$. Find the output waveform when the input is $v_{1}($ $t)=\left[20 e^{-200 t}ight] u(t)$. Use MATLAB to find...

The step response of a linear circuit is g(t) 0.25[l e150t]u(t). Find the output waveform when the input is v1(t) [20e200t]u(t). Use MATLAB to find the Laplace transforms of g(t) and v1(t). Then...

The purpose of this project is to work more with lists, looping, file I/O, functions, and dictionaries. For this assignment, you will work with real data from the web. Background Major solar storms...

Write a java program that outputs the following shape with asterisks to the console by using nested loops . ( Hint row:6 column:8) For example: Sonu * * * * * * * ** * * * * * ** **

Question: Transfer function of a complex control system is given below. T(s): = 30s + 3s + s s6+3s5+4s + 6s + 5s +3s+2 a) Observe system's stability according to coefficient tests and mention your...

11. [10] The stochastic exponential of a constant, that is, the process & defined by Et = exp xp (aB - 1/2), t for some constant a, is a martingale. a. Prove the above statement directly, that is, by...

You sell t shirts at $10 each, and you have to pay the worker at each workstation $500/day.You went and hired a student who did some market research and told you that you could increase your price to...

1. The linkage shown below is made of two identical members with lengths of 0.8 m and masses of 3 kg. The left member is connected to the ground by a pin joint, and the right member is connected to...

What role would market research play in helping businesses improve their B 2 C communications ( and result in a higher frequency of positive C 2 B interactions ) ?

Firm XYZ is planning on opening a new factory. The initial cost to build the factory is $3.5 billion , the factory will last 7 years and will have a salvage value of $1.5 billion. It plans to use...

Which of the ocean zones shown would be home to each of the following organisms: lobster, coral, mussel, porpoise, and dragonfish? For those organisms you identify as living in the pelagic...

Obtain the transfer function Vo(s)/Vi{s) for the op-amp system shown in Figure. R2 C 7i

PID control action is applied to the plant Gp(s) = s + 10/ (s + 2) (s + 5) The PID controller has the transfer function Gc(s) = Kp (1 + 1/TIs + TDs) Use the values TI = 0.2 and TD = 0.5. Plot the...

Use the MATLAB series and feedback functions to obtain the transfer functions X(s)/F(s) and X(s)/G(s) for the block diagram shown in Figure. G(s) F(s) + X(s) 4

Consider the following four correlation matrices that apply to clusters having five responses per cluster: a. b. c. d. a. Matrix A is an example of what kind of correlation structure? b. Matrix B is...

Consider again the study described in the main body of this chapter concerning the effect of an air pollution episode on pulmonary function measurements (FEV1) taken on each of K= 40 school children...

A five-year follow-up study was carried out in a certain metropolitan area to assess the relationship of diet and weight to the incidence of stomach cancer. Data were obtained on n = 2,000 subjects....