Snapsolve any problem by taking a picture. Try it in the Numerade app?
A forced undamped simple harmonic oscillator has the equation dy(t)/dt^2 + my(t) + ky(t) = f(t), where f(t) is a periodic function with period 4, and for -2 < t < 0 and 0 < t < 2, f(t) = 0. (a) Find the complex exponential Fourier series for f(t). (b) Assuming that y(t) is also a periodic function with period 4, find the complex exponential Fourier series for y(t). (c) For what values of k/m will this method of finding y(t) fail?
Added by Michael O.
Close
Step 1
(a) Show more…
Show all steps
Shyam P and 77 other Calculus 3 educators are ready to help you.
Ask a new question
Recommended Videos
An undamped forced oscillation is modeled as a nonhomogeneous ODE as follows: my′′ + ky = cosωt + 2sinωt where m = 1, k = 4, and ω is a given constant. a) Find the general solution for this nonhomogeneous ODE. Show each step of your work. Hint: you may want to discuss two cases: I) when ω does not equal the natural frequency of this system II) when ω equals the natural frequency of this system. b) Based on your solution above, how will you choose your ω in your input force to reach the case of resonance? Then show your solution in case of resonance and briefly describe or draw the behavior of your system in resonance.
Carson M.
An undamped forced oscillation is modeled as a nonhomogeneous ODE as follows: my" + ky = cos(wt) + sin(wt) where M, k, and w are all constants. a) Find the general solution for this nonhomogeneous ODE. Show each step of your work. Please use ω₀ = √(k/m), which is the natural frequency of this system, to simplify your answer. b) Based on your solution, how will you choose your ω in your input force to reach the case of resonance? Then show your solution in the case of resonance and briefly describe or draw the behavior of your system in resonance.
Madhur L.
In Exercises 1-4, the harmonic oscillator equation for y(t) is given. (a) Using HPGSystemsolver, sketch the associated direction field. (b) Using the guess-and-test method described in this section, find two nonzero solutions that are not multiples of one another. (c) For each solution, plot both its solution curve in the yu-plane and its y(t) and v(t) graphs.
Adi S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
Not finding what your looking for? Here are some other ways we can help!
Generate practice questions
Explain a concept
Create a study plan
EMAIL
PASSWORD