A critically damped, driven oscillator’s displacement x(t) satisfies the equation of motion
x¨ + 2ω0x˙ + ω20x = f0 cos ωt (1)
where ω0 is the natural frequency, and ω is the “driving frequency”.
(i) Find the particular solution to the above equation, in the form xp(t) = A cos(ωt + φ).
Your answer should clearly give the expressions for A and φ.
(ii) The homogeneous equation ¨x + 2ω0x˙ + ω20x = 0 has e−ω0t as one solution. Show, by
substitution, that the function te−βt can be the second solution. Find β in terms of ω0.
(iii) Use the above results to construct the complete solution to Eq. 1, subject to the initial
conditions x(0) = 0 = ˙x(0).
Answers
Answered by
1
see this doc hope you get it right.
you can contact me for any further queries
Attachments:
Similar questions