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example_IV_1_07

example_IV_1_07 - y ω n 2 ω n 2 ω 2 sin ω t x(0 = 0 = c...

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Example IV.1.7 - “beating” in forced response Sketch the “steady-state” response of the base-excited system shown below (with initial conditions of x(0) = x ˙ (0) = 0) for ω n . Solution From before: x(t) = c cos ω n t + s sin ω n t
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Unformatted text preview: + y ω n 2 ω n 2- ω 2 sin ω t x(0) = 0 = c x ˙ (0) = 0 = s ω n + y ω n 2 ω n 2- ω 2 ω ⇒ s = - ω ω n y ω n 2 ω n 2- ω 2 Therefore x(t) = y ω n 2 ω n 2- ω 2 [ sin ω t - ω ω n sin ω n t ]...
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example_IV_1_07 - y ω n 2 ω n 2 ω 2 sin ω t x(0 = 0 = c...

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