Answer to Question #147567 in Mechanical Engineering for Teja

Question #147567

A critically damped, driven oscillator’s displacement x(t) satisfies the equation of motion

x¨ + 2ω0x˙ + ω

0^2x = f0 cos ωt


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˙ +ω0^2x = 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).

Expert's answer

1) driving frequency = f0 cos ωt

ii) x¨ + 2ω0x˙ + ω

iii) A cos(ωt + φ).

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be the first!

Leave a comment

New on Blog