Reference no: EM13350482
Task 1
Evaluate Laplace transforms and their inverse using tables and partial fractions
1. Determine the Laplace transform of each of the following
![1709_Evaluate Laplace transforms and their inverse using tables and partial fractions.png](https://www.mywordsolution.com/CMSImages/1709_Evaluate%20Laplace%20transforms%20and%20their%20inverse%20using%20tables%20and%20partial%20fractions.png)
2. Evaluate the inverse Laplace transforms of the subsequent functions
![1948_Evaluate Laplace transforms and their inverse using tables and partial fractions1.png](https://www.mywordsolution.com/CMSImages/1948_Evaluate%20Laplace%20transforms%20and%20their%20inverse%20using%20tables%20and%20partial%20fractions1.png)
Task 2
Solve first and second order differential equations using Laplace transforms
3. Solve the subsequent first order differential equations using Laplace transforms
![1301_Evaluate Laplace transforms and their inverse using tables and partial fractions2.png](https://www.mywordsolution.com/CMSImages/1301_Evaluate%20Laplace%20transforms%20and%20their%20inverse%20using%20tables%20and%20partial%20fractions2.png)
4. Use Laplace transform to solve the subsequent second order differential equation
![1941_Evaluate Laplace transforms and their inverse using tables and partial fractions3.png](https://www.mywordsolution.com/CMSImages/1941_Evaluate%20Laplace%20transforms%20and%20their%20inverse%20using%20tables%20and%20partial%20fractions3.png)
Task 3
Model and examine engineering systems and evaluate system behaviour using Laplace transforms
5. A series LR circuit with a step input voltage will be modelled by the equation:
i(0)=0 L, R and V are constants
Use Laplace transforms to show:
![1920_Evaluate Laplace transforms and their inverse using tables and partial fractions5.png](https://www.mywordsolution.com/CMSImages/1920_Evaluate%20Laplace%20transforms%20and%20their%20inverse%20using%20tables%20and%20partial%20fractions5.png)
6. The charge in a series LCR circuit is modeled by the equation:
![1208_Evaluate Laplace transforms and their inverse using tables and partial fractions6.png](https://www.mywordsolution.com/CMSImages/1208_Evaluate%20Laplace%20transforms%20and%20their%20inverse%20using%20tables%20and%20partial%20fractions6.png)
Solve the equation in case when L=2 H, R=20?, C=0.02 F