A forced damped spring-mass system (Figure) has the following ordinary differential equation of motion: Where x =
Question:
A forced damped spring-mass system (Figure) has the following ordinary differential equation of motion:
Where x = displacement from the equilibrium position, t = time, m = 2 kg mass, α = 5 N/(m/s)2, and k 6 N/(m/s)2. The damping term is nonlinear and represents air damping. The forcing function Fα sin (ωt)has values of Fα = 2.5 N and ω = 0.5 rad/sec. The initial conditions are
Initial velocity dx/dt = 0 m/s
Initial displacement x = I m
Solve this equation using a numerical method over the time period 0 ≤ t ≤ 15 s. Plot the displacement and velocity versus time, and plot the forcing function on the same curve. Also, develop a separate plot of velocity versus displacement.
Step by Step Answer:
Numerical Methods For Engineers
ISBN: 9780071244299
5th Edition
Authors: Steven C. Chapra, Raymond P. Canale