# Transfer Function

1. Is the linear time-invariant continuous-time system with the impulse response h(t) = sin 2t for t ≥ 0 BIBO is stable? Explain.

2. Determine if the linear time-invariant continuous-time system defined by:

is stable, marginally stable, unstable, or marginally unstable. Show work.

3. Compute the steady-state response for the linear time-invariant continuous-time system with the transfer function:

when the input is x(t) = cos(t), t ≥ 0 and no initial energy.

4. A linear time-invariant continuous-time system has transfer function:

Compute the transient response resulting from the input x(t)=2cos(4t), t>=0, with zero initial conditions.

5. The response of a system to an input is:

What is the steady-state response?

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#### Solution Preview

1. Is the linear time-invariant continuous-time system with the impulse response h(t) = sin 2t for t ≥ 0 BIBO is stable? Explain.

Solution:

We can solve the BIBO stability of the impulse response if it is absolutely integrable using the integral form:

Substituting, we have:

Since both and does not have a unique value in the range of -1 to +1, then they have no unique value. Therefore, the impulse response in not integrable and therefore BIBO unstable.

2. Determine if the linear time-invariant continuous-time system defined by:

is ...

#### Solution Summary

The expert examines a linear time-invariant continuous-time system.