Find the inverse laplace transform, Applied Statistics

Q. Find the inverse Laplace transform of Y (s) = s-4/s2 + 4s + 13 +3s+5/s2 - 2s -3.

Q. Use the Laplace transform to solve the initial value problem y''+ y = cos(3t), y(0) = 1, y'(0) = 0.

3. Solve the initial value problem y'' + y = f(t); y(0) = 0; y'(0) = 1;

1903_Find the inverse Laplace transform.png


4. Recall from Chapter 4, that initial value problems of the form
ay'' + by'+ cy = f(t); y(0) = y0, y'(0) = y1;

could be used to model the motion of a mass attached to a spring. When the mass is given a sharp blow at time t = p, the forcing function can described using the Dirac delta function δ(t - p). In the special case that p = 0, y0 = 0 and y' (0) = 0, we say:
The solution to the initial value problem

ay''+ by'+ cy = (t); y(0) = 0; y'(0) = 0;

is called the unit impulse response function to the system modeled by the di erential equation.

(a) A mass attached to a spring is in its equilibrium position. After 2 seconds the mass is struck by a hammer exerting an impulse on the mass. The system is modeled by the initial value problem

y''+ y = 4(t   2); y(0) = 0; y'(0) = 0:

Find a function that describes the motion of the mass.

(b) How would the motion change in the last problem if y(0) = 1, i.e., if the mass was released one unit below its equilibrium position at t = 0?

Posted Date: 2/14/2013 1:22:52 AM | Location : United States







Related Discussions:- Find the inverse laplace transform, Assignment Help, Ask Question on Find the inverse laplace transform, Get Answer, Expert's Help, Find the inverse laplace transform Discussions

Write discussion on Find the inverse laplace transform
Your posts are moderated
Related Questions
Question Following the general methodology used by econometricians as explained in the session for week 1 (eight steps), explain how you would proceed to determine if a good com

Pneumatic Actuator Design Matrix: The range of actuator design parameters have been provisionally assessed and are presented in Table. You are required to determine the following

A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2

What would be the cutoff score to indicate a score that is in the top 15% of the scores on a test with a mean of 100 and a standard deviation of 15? This question has multiple p

Mode The mode is the value which occurs most frequently in a set of observations on the point of maximum frequency and around which other items of the set cluste


what are characteristics of a population for which it would be appropiate to use mean/median/mode

Simple Linear Regression   While correlation analysis determines the degree to which the variables are related, regression analysis develops the relationship between the var

Explain any two applications of statistics

I would like to know what the appropriate statistical test is for investigating an association between a nominal variable and an ordinal variable assuming normal distribution? It''