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
Quota sampling Under this method enumerators shall select the respondents in place of those not available, as per the quota fixed according  to guide lines   provided to them.

Linear Regression Generally, in two mutually related statistical series, the regression analysis based on graphic method. Under graphic method the values  of X and Y variable

The Null Hypothesis - H0:  The random errors will be normally distributed The Alternative Hypothesis - H1:  The random errors are not normally distributed Reject H0: when P-v

Q. Find relative maxima and minima? When finding relative maxima and minima in the Chapters absolute extrema problem, don't forget to use the first or second derivative test to

Large Sample Test for Proportion A random sample of size n (n > 30) has a sample proportion p of members possessing a certain attribute (success). To test the hypothesis that t

Steps in ANOVA The three steps which constitute the analysis of variance are as follows: To determine an estimate of the population variance from the variance that exi

Advantages of Sampling Why should we settle on a sample instead of studying the entire population?  Sampling has the following advantages over a census (study of the entire pop

The tension, T, in the tow rope pulling the car in Newtons is given in P8.  Determine the minimum length of the rope l, between A and B, so that the tension in either AB or AC equa

Consider the following game: (a) If (top, left) is a Weakly Dominant Strategy Equilibrium, then what inequalities must hold among (a, ..., h)? (b) If (top, left) is a Na

a) List down several measures of central tendency and define the difference among them? b) What do you mean by confidence interval, and why it is useful? What is a confidence lev