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# Laplace transform

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Hi,

Section 7.3 # 4,8,14,20
See attached

determine the Laplace transform of the given function.

https://brainmass.com/math/calculus-and-analysis/laplace-transform-213409

#### Solution Summary

This provides examples of determining the Laplace transform.

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## Laplace Transformations and Inverse Laplace Transformations

1. Find the Laplace transform of 6 cos t + 2e −3t .

2. Find the Laplace transform of 2 cosh t + 2t 3.

3. Find the Laplace transform of 2te −3t.

4. Find the inverse Laplace transform of s/s+2.

5. Find the inverse Laplace transform of 1/s+5.

6. Find the inverse Laplace transform of 1/( s + 5 ) ( s 2 + 1).

7. The voltage and current in the Laplace domain for a certain system is given by V (s) = 1/12 1/s^2 +3, I(s) = s/s^2+3. Is this system best described as resistive, capacitive, or inductive?

8. The voltage and current in the Laplace domain for a certain system is given by V(s) = 9 1/s^2+16, I(s) = 1/s^2+16. Is this system best described as resistive, capacitive, or inductive?

9. For a second order RLC circuit, in the s-domain s^2 + R/L s + 1/LC = 0. If R = 2 Ω, C = 2 F, and L = 16 H , is the system damped? If so, how? Characterize the behavior of the system.

10. A resistor and inductor are connected in series with a voltage source v ( t ) = 20sin 30t .If R = 12 Ω, L = 4 H, find the total response of the current. Assume there is initially no current. Identify the transient solution

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