Find the impulse response of a causal LTI system represented by the following differential equation: $\frac{d^2y(t)}{dt^2} + 4\frac{dy(t)}{dt} + 4y(t) = x(t)$ $(1 - t)e^{-2t}u(t)$ $te^{-2t}u(t)$ $\delta(t) + 4(t - 1)e^{-2t}u(t)$ $(1 - 2t)e^{-2t}u(t)$
Added by Matthew D.
Close
Step 1
The given differential equation is: dy/dt^2 = (1 - te^2ut)te^-2tu(t) + (8t + 4t^1e^2ut) + (12tc - 2ut) To write it in the standard form, we need to move all the terms to the left-hand side and set it equal to zero: dy/dt^2 - (1 - te^2ut)te^-2tu(t) - (8t + Show more…
Show all steps
Your feedback will help us improve your experience
Satish Kumar and 66 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
For each impulse response of a continuous-time LTI system, determine (1) whether or not the system is causal and (2) whether or not the system is stable. Justify your answers. a) h(t) = e^(-2t)u(t-1) b) h(t) = e^(2t)u(-t+1) c) h(t) = e^(4t)cos(2t)u(t) d) h(t) = cos(100Ď€t)u(t+1)
Adi S.
Obtain the impulse response of a system modeled by the differential equation \[ 2 \frac{d y}{d t}+y(t)=x(t) \] where $x(t)$ is the input and $y(t)$ is the output.
The impulse response of an LTI system is h(t) = 3e^(-2t)u(t). Find the response of the system for the input x(t) = 2e^(-3t)u(t).
Sri K.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD