Question: In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f (t) = te -t

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t).

f (t) = te^-t sin² t

THEOREM 2 Differentiation of Transforms If f(t) is piecewise continuous for t

0 and f(t)| Mect as t +o, then L{-tf(t)} = F' (s)

THEOREM 2 Differentiation of Transforms If f(t) is piecewise continuous for t 0 and f(t)| Mect as t +o, then L{-tf(t)} = F' (s) for sc. Equivalently, f(1) = '{F(s)} = --L' {F'(s)}. Repeated application of Eq. (6) gives for n 1, 2, 3, .... = L{t" f(t)} = (-1)"F(n) (s) (6) (7) (8)

Step by Step Solution

★★★★★

3.33 Rating (141 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Lsint 1 cos 2t2 L1 c... View full answer

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 First Course Differential Equations Questions!

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f (t) = t sin 3t THEOREM 2 Differentiation of Transforms If f(t) is piecewise continuous for t 0...

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f(t) = e1 31 t -1

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f(t) = sint t

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f (t) = te 2t cos 3t THEOREM 2 Differentiation of Transforms If f(t) is piecewise continuous for...

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f (t) = t 2 cos 2t THEOREM 2 Differentiation of Transforms If f(t) is piecewise continuous for t...

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f(t)= = 1 - cos 2t t

In Problems 15 through 22, apply either Theorem 2 or Theorem 3 to find the Laplace transform of f (t). f(t) = et - e-t t

7 L 'LJ' :! OR? T * [4 ! 715 n rip ti up qi x r' '=(91nmnvmic :I;J = D Spring 2017 Stony Brook University Snliyaisachi Muklusrjeo, Matthew Dnnnonlmrg Problem Set 6 Differential Equations with Linear...

a. Find the Laplace transform of the given function. Use Table 2.2 when applicable. b. Confirm the result of (a) in MATLAB. \(t^{2} \sin \left(\frac{1}{2} t ight)\) TABLE 2.2 Laplace Transform Pairs...

a. Find the Laplace transform of the given function. Use Table 2.2 when applicable. b. Confirm the result of (a) in MATLAB. \(\sin ^{2} t\) TABLE 2.2 Laplace Transform Pairs No. f(t) F(s) 1 Unit...

Find all initial conditions such that (x2 4x)y' = (2x 4)y has no solution, precisely one solution, and more than one solution.

Differentiate between matrix and project structures.

In the multiattribute location model, what is the rationale for weighting subjec tive factors?

18. Let X and Y be independent exponential random variables having respective rates and . Let /, independent of X, Y, be such that with probability ^ and define by = with probability X, \i I = \ -...

Briefly describe the difference between predicting a value of y and estimating the expected value of y.

Will the prediction interval always be wider than the estimation interval for the same value of the independent variable? Briefly explain.

Refer to Exercise 16.45. Estimate with 95% confidence the mean time spent watching or reading news on the Internet for the population of people who have completed 12 years of education. In exercise...

The equality of the accounting equation can be proven by preparing a Answer A. trial balance. B. journal. C. general ledger. D. T-account

What would be a non-value added activity of a non-profit homeless shelter? This means the activity would be unnecessary and disposable or it could be necessary, but inefficient.

Balancw sheet The account balances of A-One Travel Service for the yoar ended August 11, 20r6, follow: Cathdividendt of 531,500 ware ptid during the year. Rotwined earnings as of September 1, 20rs,...