Please help me to understand this concept with maybe one or two examples. THANKS

Question

Please help me to understand this concept with maybe one or two examples. THANKS!

The differential equations for some mass spring systems are given below. Which of these systems have resonance? y"(t) + 16y = 8 cos 4t, y(0) = 2, and y'(0) = -3 y" + 8y' + 16y = 8 cos 4t, y(0) = 0. and y'(0) = 4 y" + l6y = 2c-3a cos 4t, y(0) = 2 and y'(0) = 3 y"(t) + 25y - 2 sin 5t, y(0) = -3 and y'(0) = 0 y"(t) + 25y = 5 sin 2t, y(0) = -3 and y'(0) = 0 y" + 2y' + 20y = 5 sin(4t), y(0) = 1, and y'(0) = 4 y" + 16y = 3e-2t sin(4t), y(0) = 2, and y'(0) = 0. The solutions of some mass spring systems are given below. Which of these systems exhibit resonance? y(t) = 5e-t sin 4t + 6 sin 4t y(t) = 5t sin 4t + 6 sin 4t y(t) = 8 cos 3t - 5 sin 3t + 2 sin 4t y(t) = t(2 cos 3t + 4 sin 3t) + 5 sin 6t.

Explanation / Answer

http://mathworld.wolfram.com/First-OrderOrdinaryDifferentialEquation.html

Can be helpful :)

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