Question

consider the question:
x(t) = cos(2Pi*t) + sin(5t)
is this system periodic? My work is below

Answer 1

Where is your work?

Answer 2

\[T = \frac{ 2\pi }{ \omega }\]
\[T_1 = \frac{ 2\pi }{ 2\pi } = 1\]
\[T_2 = \frac{ 2\pi }{ 5 }\]

\[\frac{ T_1 }{ T_2 } = \frac{ 5 }{ 2\pi } \]

since the last is irrational then its aperiodic?

Answer 3

a system needs to satisfy x(t) = x(t+T) to be periodic since T1/T2 is irrational thus the system is aperiodic

Answer 4

yes, that is correct.