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
Q. 1 a) Describe the important quantitative techniques used in public system management. (10) b) Do you think the day will come when all decisions are made with the assistance of

To use Linear Programming for solving the following inequalities. Following Twin Conditions (as mandated by the Indian Regulatory Authority) Twin Condition I for TV Broadcasters

difference between large sample test and small sample test

what is the independent variable in how energetic do people feel after drinking different types of soft drints?

Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used  for the same purpose i.e. when  the values are differing  widely in their magnitude

what is the use of applied statistic in our daily routin life

Sampling Error  It is the difference between the value of the actual population parameter and the sample statistic. Samples are used to arrive at conclusions regarding the p

fixed capacitor and variable capacitor


Define sampling unit and population for selecting a random sample in every case. a) 100 voters from a constituency b) 20 stocks of National Stock Exchange c) 50 account ho