Question

For each of the following systems, specify whether or not the system is: (i) linear and/or (ii) time-invariant.

A. y(t) = 3x(t) + 1
B. y(t) = 3sin(t) x(t)
C. dy/dt + t y(t) = x(t)
D. dy/dt + 2y(t) = 3dx/dt

Answer 1

System A is linear and time-invariant. System B is neither linear nor time-invariant. System C and D are linear but not time-invariant.

Step-by-step explanation:

The system A is linear because it follows the form y(t) = mx(t) + c, where m and c are constants. The system is also time-invariant because the outputs do not change with time.

The system B is neither linear nor time-invariant because it involves a sinusoidal function, which is not a linear function.

The system C is linear because it follows the form dy/dt + t y(t) = x(t), which is a linear differential equation. However, it is not time-invariant because the presence of time variable t affects the system's behavior.

The system D is linear because it follows the form dy/dt + 2y(t) = 3dx/dt, which is a linear differential equation. However, it is not time-invariant because the presence of time variable t affects the system's behavior.