Determine the values of the appropriate parameters needed to give the systems governed by the following second-order linear constant-coefficient differential equations the damping parameters and natural frequencies stated:

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(a) (b) dx + dt dx dt (c) a a dx 2 dt dx dt d.x + a + bx = 0, y = 2, w = dt dx dt + bx = 0, = 0.25, w = 2 +4- + cx = 0, y = 0.5, w = 2 dx (d) px +q dx dt dt +q + 6x = 0, = 1.2, = 0.2