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Unformatted text preview: y 00 ( t ) + 4 y ( t ) + 13 y ( t ) = 13 x ( t ) where the initial conditions are all zero, y 00 (0) = 0 , y (0) = 0 , and y (0) = 0 . The input is the unit step x ( t ) = u ( t ) . Find y ( t ) . 4. For each of these assertions, determine whether they are true or false. Provide an argument for your conclusion. Remember that an unstable system has poles either in the righthalf plane (diverging solutions) or on the jω axis (oscillating or constant solutions). a) Let h ( t ) be the impulse response of a stable, causal system. Then d dt h ( t ) is also stable. b) Let h ( t ) be the impulse response of a stable, causal system. Then Z t∞ h ( τ ) dτ must be unstable. c) H ( s ) is the transfer function of a stable, causal system. The zeros of H ( s ) must be in the righthalf plane for the inverse system H inv ( s ) to be stable....
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 Spring '09
 Levan
 Laplace

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