5. (0) = 1 is subject to a step force of F(t) = 2H(t) N, where H(t) is the Heaviside step function. Use Duhamel's integral to find the total response x(t) of this system if m = 4, k = 16, and c = 2. All units are SI.
Added by Kathleen R.
Close
Step 1
Step 1: Write the equation of motion The equation of motion for this system can be written as: m*x''(t) + c*x'(t) + k*x(t) = F(t) Show more…
Show all steps
Your feedback will help us improve your experience
Krystal K and 79 other Physics 101 Mechanics 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
(a) Using integration by parts evaluate the integral: F(s) = ∫₀∞ e^{-st} t u(t) dt to show that the Laplace transform of tu(t) is equal to 1/s². (Remember: e^{-st} → 0 as t → ∞) u(t) is the unit step function (= 1 for t ≥ 1; = 0 for t < 0)
Madhur L.
Consider the following IVP: y'' - 4y' + 5y = g(t), y(0) = 0, y'(0) = 1 (a) Find the transfer function H(s) for the system, the impulse response function h(t) for the system, and give a general formula for the solution for the IVP. (b) If g(t) = 10, find the solution to the IVP using your formula from part a.
Sri K.
The response x(t) of a system to a forcing function u(t) is determined by the following differential equation d^2x/dt^2 + 2dx/dt + 5x = 3du/dt + 2u (a) Determine the transfer function characterizing the system. (b) Write down the characteristic equation of the system.
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