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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 right-half 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 right-half plane for the inverse system H inv ( s ) to be stable....
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- Spring '09