4.12 ASSIGNMENT PROBLEMS

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1. Write a Scilab program to implement the following equation to calculate the value of x.

2. Write a Scilab program to implement the following equation to calculate the value of x.

3. Write a Scilab program to integrate the area under the function below using a numerical method, such as Simpson's rule. Find the area from 1 to 2.

4. Convert the third order differential equation below to state equation form. With a numerical method of your choice, find the state of the system 1 second later. Show all calculations.

5. The differential equation below describes a first order system that starts with an initial value of k=20. Find the state at two milliseconds using a) explicit integration, b) first order numerical integration and c) Runge-Kutta integration. For the numerical methods use a timestep of h=0.001s. ----> The final results must be put in a table for easy comparison.

6. Explicitly solve the following differential equation. Verify the result numerically.

7. Given the mass spring damper system below a) develop the state equations, and b) estimate the steady state response. Consider gravity.

8. Write the differential equations AND state equations for the systems below.