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Question 2.4: Consider a SDOF system shown in Figure 2.2. It undergoes und...

Consider a SDOF system shown in Figure 2.2. It undergoes underdamped free vibrations. The mass = 40 kNs²/m and stiffness k = 3750 kN/m. The initial conditions are given as: x(0) = 0.01 m, \dot{x}(0) = 0.1 m/s. Plot the influence of 0, 5% and 10% damping on the displacement–time history.

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Annotation 2022-10-23 174152
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The response of a SDOF system can be determined using MATLAB for different damping ratios. The results are plotted in Figure 2.9. The amplitude of displacement decreases with increase in damping. In an undamped system (ξ = 0%), the amplitude
remains constant and the system vibrates indefinitely. Even with 5% damping, there is
significant drop in the amplitude of vibration.

Annotation 2022-10-23 173933

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Question: 2.1

Consider a SDOF system shown in Figure 2.1. It undergoes undamped free vibrations. The mass = 40 kNs²/m, stiffness k = 3500 kN/m. Determine the natural frequency and natural period of vibration. The initial conditions are given as: x(0) = 0.01 m, x(0) = 0.1 m/s. Hence, plot a graph of ...

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Question: 2.5

Consider a SDOF system shown in Figure 2.2. It undergoes underdamped free vibrations. The mass = 40 kNs²/m, stiffness k = 3750 kN/m and c = 50 kNs/m. The initial conditions are given as: x(0) = 0.01 m, x(0) = 0.1 m/s. Plot the inertia, damping and spring forces. ...

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In the undamped SDOF system of Example 2.1, plot the response for different initial conditions as follows: Case 1: x(0) = 0.01 m, x(0) = 0.1 m/s Case 2: x(0) = 0, x(0) = 0.1 m/s Case 3: x(0) = 0.01 m, x(0) = 0 ...

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Question: 2.3

Consider a SDOF system shown in Figure 2.1. It undergoes underdamped free vibrations (damping ξ = 5%). The mass = 5 kNs²/m, stiffness k = 100 kN/m. The initial conditions are given as: x(0) = 0.02 m, x(0) = 0.05 m/s. Plot the displacement–time history and velocity time history using MATLAB. ...

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The plots of the displacement response and velocit...