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An SDOF system has the following properties: m = 0.2, k = 10, and = 0.06. No initial conditions. Determine the response u(t) (up to t = 6.0 second) of the system due to the excitation p(t)= 10sin(nt/0.5), 0≤ t ≤0.75, by the following methods: 1. Analytical solution. 2. Central difference method using two time steps, i.e., At = 0.1 sec and At = 0.01 sec, respectively. Compare your numerical results with analytical results. Discuss the influence of At on your results.

An SDOF system has the following properties: m = 0.2, k = 10, and = 0.06. No initial conditions. Determine the response u(t) (up to t = 6.0 second) of the system due to the excitation p(t)= 10sin(nt/0.5), 0≤ t ≤0.75, by the following methods: 1. Analytical solution. 2. Central difference method using two time steps, i.e., At = 0.1 sec and At = 0.01 sec, respectively. Compare your numerical results with analytical results. Discuss the influence of At on your results.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question 3: An SDOF system has the following properties: m = 0.2, k = 10, and = 0.06. No initial conditions. Determine the response u(t) (up to t = 6.0 second) of the system due to the excitation p(t)= 10sin(πt/0.5), 0≤ t ≤0.75, by the following methods: 1. Analytical solution. = 2. Central difference method using two time steps, i.e., At = 0.1 sec and At 0.01 sec, respectively. Compare your numerical results with analytical results. Discuss the influence of At on your results.
Transcribed Image Text:Question 3: An SDOF system has the following properties: m = 0.2, k = 10, and = 0.06. No initial conditions. Determine the response u(t) (up to t = 6.0 second) of the system due to the excitation p(t)= 10sin(πt/0.5), 0≤ t ≤0.75, by the following methods: 1. Analytical solution. = 2. Central difference method using two time steps, i.e., At = 0.1 sec and At 0.01 sec, respectively. Compare your numerical results with analytical results. Discuss the influence of At on your results.
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Given:

mass, m=0.2 

stiffness, k=10

ζ=0.06

To find:

Analytical solution

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