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Unformatted text preview: u = 0. The system, therefore, has a natural frequency of 2 / = = m k (radians/sec). Hence, resonance would occur if 2 = = . 7. (a) The 3 equilibrium solutions are: y = 0 (stable), y = T (unstable), and y = K (stable). (b) The population would die out if 0 < y < T , its size would become stable if y 0 T . The population would never increase without bound. 8. The complementary solution is t t c e t C e C t y 3 2 3 1 ) ( + = . Therefore, the particular solution should have the form: t A t A e t A A t A t A t Y t sin cos ) ( 6 5 3 2 4 3 2 2 1 + + + + + = ....
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