7.2E: The Inverse Laplace Transform (Exercises)

Q7.2.1

1. Find the inverse Laplace transform.

1. \( {3\over(s-7)^4}\)
2. \( {2s-4\over s^2-4s+13}\)
3. \( {1\over s^2+4s+20}\)
4. \( {2\over s^2+9}\)
5. \( {s^2-1\over(s^2+1)^2}\)
6. \( {1\over(s-2)^2-4}\)
7. \( {12s-24\over(s^2-4s+85)^2}\)
8. \( {2\over(s-3)^2-9}\)
9. \( {s^2-4s+3\over(s^2-4s+5)^2}\)

2. Find the inverse Laplace transform.

1. \( {2s+3\over(s-7)^4}\)
2. \( {s^2-1\over(s-2)^6}\)
3. \( {s+5\over s^2+6s+18}\)
4. \( {2s+1\over s^2+9}\)
5. \( {s\over s^2+2s+1}\)
6. \( {s+1\over s^2-9}\)
7. \( {s^3+2s^2-s-3\over(s+1)^4}\)
8. \( {2s+3\over(s-1)^2+4}\)
9. \( {1\over s}-{s\over s^2+1}\)
10. \( {3s+4\over s^2-1}\)
11. \( {3\over s-1}+{4s+1\over s^2+9}\)
12. \( {3\over(s+2)^2}-{2s+6\over s^2+4}\)

3. Find the inverse Laplace transform.

1. \( {-s^2+s+5\over s^3+s^2-4s-4}\)
2. \( {5s-4\over s^3-s^2-2s}\)
3. \( {3s^2+2s+1\over(s^2+1)(s^2+2s+2)}\)
4. \( {-s+1\over(4s^2+1)(s^2+1)}\)
5. \( {34-17s\over(2s-1)(s^2-2s+5)}\)
6. \( {s-6\over(s^2-1)(s^2+4)}\)
7. \( {3s+2\over(s^2+1)(s-1)^2}\)