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
Theories of Business forecasting

Accident proneness  A personal psychological issue which affects the individual's probability of suffering the accident. The concept has been studied statistically under the num

slope parameter of 1.4 and scale parameter of 550.calculate Reliability, MTTF, Variance, Design life for R of 95%

You will recall the function pnorm() from lectures. Using this, or otherwise, Dteremine the probability of a standard Gaussian random variable exceeding 1.3.  Using table(), or

We are interested in assessing the effects of temperature (low, medium, and high) and technical configuration on the amount of waste output for a manufacturing plant. Suppose that

how do you find if two way or one way

To determine the proportion of people in your town who are smokers, it has been decided to poll people at one of the following local spots: (a) the pool hall; (b) the bowling alley

Cluster Sampling Here the population is divided into clusters or groups and then Random Sampling is done for each cluster. Cluster Sampling differs from Stratified Sampl

JAR 21 SUPPLEMENTAL TYPE CERTIFICATION JAR 21 Part E introduces the need for Supplemental Type Certification when a manufacturer wishes to make major changes to the Type Desig

The Harmonic Mean is based on the reciprocals of numbers averaged. It is defined as the reciprocal of the arithmetic mean of the reciprocal of the given individual observations. Th