Let the input to a system be $u(t) = \cos(t)\sin(t)$ and the output be $y(t) = \cos^2(t) - \sin^2(t)$. Can this system be linear? Justify your answer.
Added by Rachel S.
Close
Step 1
That is, if $y_1(t)$ is the output for input $u_1(t)$ and $y_2(t)$ is the output for input $u_2(t)$, then for any constants $a$ and $b$, the output for input $au_1(t) + bu_2(t)$ is $ay_1(t) + by_2(t)$. Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 75 other Physics 102 Electricity and Magnetism educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Problem 1.1. Is the system y(t) = cos(x(t)) is Linear 1.2 Is it Time Invariant? Beginning of the solution of 1.1: y1(t) = cos(x1(t)) y2(t) = cos(x2(t)) y3(t) = cos(a1 x1(t) + a2 x2(t)) Is y3(t) = y1(t) + y2(t) ?? If yes then the system in linear, If NO then the system is nonlinear. You need to explain and prove your answer.... Beginning of the solution of 1.2: y(t) = cos(x(t)) y2(t) = cos(x(t - t0)) Is y2(t) = y(t - t0) ??? You need to explain and prove your answer....
Adi S.
The system y(t) = t^2 * x(2t) is linear and time-invariant. Justify your answer.
Q 2. (a) Determine if the following systems are linear, memoryless, causal, stable and time-invariant. Justify your answers (no points will be given without justification). [Attempt any three] (i) y(t) = ∫₀ᵗ x(t - τ)e⁻ᵔdτ (ii) y(t) = x(sin(t)) (iii) y(t) = (2 + sin(t))x(t - 1) (iv) y(t) = dx(t)/dt (v) y(t) = (x(t + 1))* (vi) y(t) = x(t)u(-t) (b) Prove that the following systems are linear but time varying. (i) y(t) = t²x(t - 1) (ii) y(t) = Odd{x(t)}
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD