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25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d²x dx + c + kx = 0 m dr dt displacement from equilibrium position (m), 1 = time (s), m = 20-kg mass, and c = the damping coefficient (N s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m. The initial velocity is zero, and the initial displacement x = 1 m. Solve this equation using a numerical method over the time period 0

25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d²x dx + c + kx = 0 m dr dt displacement from equilibrium position (m), 1 = time (s), m = 20-kg mass, and c = the damping coefficient (N s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m. The initial velocity is zero, and the initial displacement x = 1 m. Solve this equation using a numerical method over the time period 0

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d²x dx + c- + kx = 0 dt m- dr where x = displacement from equilibrium position (m), 1 = time (s), m = 20-kg mass, and c = the damping coefficient (N s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m. The initial velocity is zero, and the initial displacement x = 1 m. Solve this equation using a numerical method over the time period 0 <I< 15 s. Plot the displacement versus time for each of the three values of the damping coefficient on the same curve. FIGURE P25.16 k m
Transcribed Image Text:25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d²x dx + c- + kx = 0 dt m- dr where x = displacement from equilibrium position (m), 1 = time (s), m = 20-kg mass, and c = the damping coefficient (N s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m. The initial velocity is zero, and the initial displacement x = 1 m. Solve this equation using a numerical method over the time period 0 <I< 15 s. Plot the displacement versus time for each of the three values of the damping coefficient on the same curve. FIGURE P25.16 k m
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