Question

Let a signal a1 sin (ω1 t + φ1) be applied to an astable LTI system. The corresponding output is a2 F sin (ω2 t + φ2). Then which of the following is correct?

(a) F is not necessarily a sine or cosine function but must be periodic with ω1=ω2

(b) F must be a sine or cosine function with a1 = a2

(c) F must be a sine function with ω1=ω2 and φ1 = φ2

(d) F must be a sine or cosine function with ω1=ω2

I got this question in a national level competition.

The query is from Characterization and Nature of Systems topic in portion Laplace Transform and System Design of Signals and Systems

Answer 1

The correct option is (b) F must be a sine or cosine function with a1 = a2

The explanation: We can infer that the output of an LTI system has the same function sine or cosine with the same frequency and different phase. Hence F must be a sine or cosine function with a1 = a2.