Consider a system governed by the following equations

dx1(t)/dt = x2(t) - x1(t)

dx2(t)/dt = x1(t) - x2(t)

The initial conditions are such that x1(0)

Question

Consider a system governed by the following equations

dx1(t)/dt = x2(t) - x1(t)

dx2(t)/dt = x1(t) - x2(t)

The initial conditions are such that x1(0) < x2(0) < ∞. Let x1f = lim(t→∞) x1(t) and x2f = lim(t→∞) x2(t). Which one of the following is true?

Accepted Answer

x1f = x2f < ∞. The system of equations describes a coupled linear system where both variables approach the same limit over time due to their symmetric behavior. Given the initial condition that x1(0) is less than x2(0), both variables converge to the same finite value as time approaches infinity.

Consider a system governed by the following equations dx1(t)/dt = x2(t) - x1(t) dx2(t)/dt = x1(t) - x2(t) The initial conditions are such that x1(0) < x2(0) < ∞. Let x1f = lim(t→∞) x1(t) and x2f = lim(t→∞) x2(t). Which one of the following is true?

Solution

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