Question

The LTI system is said to be initially relaxed system when

• A. Zero input produces zero output
• B. Zero input produces non-zero output
• C. Zero input produces an output equal to unity
• D. Zero input produces an infinite output

Hint:

"Initially relaxed" implies all internal memory/storage elements (like capacitors, inductors, delay units) have zero initial values.
For such a system, the output is solely due to the input applied from that point on.

Answer 1

The Correct Option is A

An LTI system is "initially relaxed" or "at rest" if all its initial conditions are zero before an input is applied. This means there is no stored energy in the system. A consequence of being initially relaxed is that if the input to the system is zero for all time (\(x(t)=0\) or \(x[n]=0\)), then the output will also be zero for all time (\(y(t)=0\) or \(y[n]=0\)). This is known as the zero-input zero-output (ZIZO) property for a system at rest. If a zero input produces a non-zero output, it indicates the presence of non-zero initial conditions. \[ \boxed{\text{Zero input produces zero output}} \]