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Figure 1 below depicts the popular Spring-Mass-Damper system in which mis the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 ➡ x k in £ с m →F(t) Figure 1: The Spring-Mass-Damper system for Question 10. N/m. Moreover, denote by x(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t) = Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE:

Figure 1 below depicts the popular Spring-Mass-Damper system in which mis the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 ➡ x k in £ с m →F(t) Figure 1: The Spring-Mass-Damper system for Question 10. N/m. Moreover, denote by x(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t) = Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Figure 1 below depicts the popular Spring-Mass-Damper system in which mis the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 ➡ x k in £ с m Figure 1: The Spring-Mass-Damper system for Question 10. N/m. Moreover, denote by x(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t) = Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE: d²x dx m. + c +kx = dt² dt →F(t) F(t). (1) dt Assume that x(0) = 0.01 m and (0) = 0.0. Your duty as an engineer is to analyse this Spring- Mass-Damper system by fulfilling the following requirements: a) Establish the spring displacement trajectory r(t) by solving analytically the ODE equation (1) modelling the Spring-Mass-Damper. b) Using the analytical results obtained from part a), plot the displacement x(t) and the rate of change of the displacement (velocity) da(t). Each plot is with a horizontal time axis and a vertical magnitude axis. All the plots are in the interval of 0 ≤ t ≤7 where 7 ≥ 4. Note that direct copy of plots generated from computers/machines is not accepted.
Transcribed Image Text:Figure 1 below depicts the popular Spring-Mass-Damper system in which mis the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 ➡ x k in £ с m Figure 1: The Spring-Mass-Damper system for Question 10. N/m. Moreover, denote by x(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t) = Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE: d²x dx m. + c +kx = dt² dt →F(t) F(t). (1) dt Assume that x(0) = 0.01 m and (0) = 0.0. Your duty as an engineer is to analyse this Spring- Mass-Damper system by fulfilling the following requirements: a) Establish the spring displacement trajectory r(t) by solving analytically the ODE equation (1) modelling the Spring-Mass-Damper. b) Using the analytical results obtained from part a), plot the displacement x(t) and the rate of change of the displacement (velocity) da(t). Each plot is with a horizontal time axis and a vertical magnitude axis. All the plots are in the interval of 0 ≤ t ≤7 where 7 ≥ 4. Note that direct copy of plots generated from computers/machines is not accepted.
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