Assignment 3 BDA34003
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Transcript of Assignment 3 BDA34003
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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)
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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.
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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.