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Chapter 7: Q14E (page 404)

Find the Laplace transform of.f(t)=鈭�0tevsin(t鈭�v)dv

Short Answer

Expert verified

The Laplace transformation of鈭�0tevsin(t鈭�v)dvis1(s2+1)(s鈭�1).

Step by step solution

01

Given that,

f(t)=鈭�0tevsin(t鈭�v)dv

02

Applying the Convolution Theorem

g鈰�h=鈭�0tg(t鈭�v)h(v)dvg(t)=sintg(s)=1s2+1h(t)=etg(s)=1s鈭�1

03

Step 3: Simplify

L[g鈰�h]=g(s)鈰�h(s)=1s2+1鈰�1s鈭�1=1(s2+1)(s鈭�1)

Hence,

f(s)=1(s2+1)(s鈭�1)

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Most popular questions from this chapter

In Problems 25 - 32, solve the given initial value problem using the method of Laplace transforms.

z''+3z'+2z=e-3tu(t-2)z(0)=2,z'(0)=-3

In Problems 11鈥�20, determine the partial fraction expansion for the given rational function.s2鈭�26s鈭�47(s鈭�1)(s+2)(s+5)

In Problems 1鈥�19, use the method of Laplace transforms to solve the given initial value problem. Here x鈥�, y鈥�, etc., denotes differentiation with respect to t; so does the symbol D.

x''+y=1;x(0)=1,x'(0)=1x+y''=-1;y(0)=1,y'(0)=-1

In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]


3t4-2t2+1

Determine the inverse Laplace transform of the given function.


1s5.
See all solutions

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