Test: BIBO Stability - Electrical Engineering (EE) MCQ

Stability implies that a bounded input should give a bounded output. In a,b,d there are regions of x, for which y reaches infinity/negative infinity. Thus the sin function always stays between -1 and 1, and is hence stable.

The integrator system keep accumulating values and hence may become unbounded even for a bounded input in case of an impulse.

The odd function will have zero area over all real time space.

The system turns out to be unstable. Only if it is zero/finite it is stable.

 If w is a complex number with Im(w) < 0, we could have an unstable situation as well. Hence, we cannot conclude [no constraints on w given].

The integral of the system from -inf to +inf equals to a finite quantity, hence it will be a stable system.
If the ouput is constant, like: h(t) = exp(-jwt) than we can say w is a complex number with Im(w) < 0, we could have an unstable situation as well. Hence, we cannot conclude [no constraints on w given].

Even if we have a bounded input as n tends to inf, we will have an unbounded output. Hence, the system resolves to be an unstable one.

The system will be a purely oscillatory system with no damping involved.

Given system equation

Taking Laplace transform

16s²c(s) – 8s c(s) + 1c(s) = R(s)
Transfer function 
Since the poles are positive real, the system is unstable and the output tends towards x.
∴ Option 4 is the suitable response.