BDA34003

Assignment 3

1. Spring constant k is 1unit and the mass is 1 unit.

*Write down the dynamics system equation.

*Analyze the lowest natural frequency of the system and illustrate the corresponding

vibration mode shape by using:

- Standard Matrix Iteration (Inverse Power Method)

- Power Method (Matrix Iteration Method)

2. Solve the following initial value problem and given that y(0) = 0, at

- 0 x 1, with h = 0.2

- 0 x 2, with h = 0.4

By using Runge-Kutta Classical method

dy/dx = 4x(4y - 1)

BDA34003

3. The initial temperature of the material is at room temperature is 25oC. At one end (point

A) is heated while another end (point E) is attached to a cooler system. Thermal

diffusivity is 10mm2/s.

- Propose an explicit finite difference equation to find the transient temperature of the

bar of point A, B, C, D and E for every 4 seconds

- Draw the finite difference grid of point A, B, C, D and E up to 8 seconds.

- Determine the temperatures of point A, B, C, D and E at 8 seconds.

BDA34003

4. A string (2 unit length) is hold on its ends. The tension to the mass density ratio is 9kg/m

with a tension 50 N. This string will be assessed in 5 points (equally distributed) .To

vibrate the string, initial displacement and velocity are applied along the longitudinal axis.

The initial data of the displacement and velocity are given.

- Propose explicit finite difference equations and illustrate the molecule graphs

- Illustrate the analysis grid to determine the displacements of all assessment points (A,

B, C, D, E), to analyze the displacement of the string at t=0, t = 0.01 s and t = 0.02 s

- Determine the displacements of all points at, t = 0.01 s and t = 0.02 s.

- Based on your results (c), illustrates the strings at t=0, t = 0.01 s and t =0.02 s.