Question: The following ordinary differential equation describes the motion of a damped spring-mess system (Figure): where x = displacement from the equilibrium position, t = time,
The following ordinary differential equation describes the motion of a damped spring-mess system (Figure):
-1.png)
where x = displacement from the equilibrium position, t = time, m = 1 kg mass, and α = 5 N/(m/s)2. The damping term is nonlinear and represents air damping.
The spring is a cubic spring and is also nonlinear with b = 5 N/m3. The Initial conditions are
Initial velocity dx/dt = 0.5 m/s
Initial displacement x = 1 m
Solve this equation using a numerical method over the time period 0 ≤ t ≤ 8 s. Plot the displacement and velocity versus time and plot the phase-plane portrait (velocity versus displacement) for all the following cases:
(a) A similar linear equation
-2.png){kind=small}
(b) The nonlinear equation with only a nonlinear spring term
-3.png){kind=small}
(c) The nonlinear equation with only a nonlinear damping term
-4.png)
(d) The full nonlinear equation where both the damping and spring terms are nonlinear
-5.png)
dx dx + br' = 0 +a di? di
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This problem can be solved with MATLAB Damped spring mass system mass m1 kg damping nonlinear a absdxdt dxdt a2 Nms2 spring nonlinear bx3 b5 Nm3 MATLA... View full answer
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