Question:
The following differential equation governs the evolution of variable \(x(t)\) with time \(t, t \geq 0\).
\(\frac {d^2x}{dt^2} + 4x = e^{-t}\)
Given the initial conditions \(x = 0\) and \(\frac {dx}{dt} = 0\) at \(t = 0\), the value of \(x\) at \(t =\frac {\pi}{8}\) is _____ . (Rounded off to 3 decimal places)
The following differential equation governs the evolution of variable \(x(t)\) with time \(t, t \geq 0\).
\(\frac {d^2x}{dt^2} + 4x = e^{-t}\)
Given the initial conditions \(x = 0\) and \(\frac {dx}{dt} = 0\) at \(t = 0\), the value of \(x\) at \(t =\frac {\pi}{8}\) is _____ . (Rounded off to 3 decimal places)
\(\frac {d^2x}{dt^2} + 4x = e^{-t}\)
Given the initial conditions \(x = 0\) and \(\frac {dx}{dt} = 0\) at \(t = 0\), the value of \(x\) at \(t =\frac {\pi}{8}\) is _____ . (Rounded off to 3 decimal places)
Updated On: Sep 26, 2024
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Correct Answer: 0.064
Solution and Explanation
The answer is: 0.064 or 0.065 (approx.)
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