求解具有斜坡力函数的常微分方程

计算一个纯斜坡响应.

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sol = DSolveValue[{x''[t] + a^2 x[t] == Ramp[t - a], x[0] == 0, x'[0] == 0}, x[t], t, Assumptions -> a > 0] // FullSimplify

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绘制参数 a 取不同值时解的图形.

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Plot[Table[sol, {a, 1, 2, 0.3}] // Evaluate, {t, -1, 15}, Filling -> Axis]

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结合斜坡与冲击力.

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sol = DSolveValue[{x''[t] + a^2 x[t] == Ramp[t - a] + DiracDelta[t - 2 a], x[0] == 0, x'[0] == 0}, x[t], t, Assumptions -> a > 0] // FullSimplify

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Plot[Table[sol, {a, 1, 2, 0.3}] // Evaluate, {t, -1, 15}, Filling -> Axis]

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