As indicated by the cart-with-flywheel example discussed in this section, an unbalanced rotating machine part typically results
Question:
As indicated by the cart-with-flywheel example discussed in this section, an unbalanced rotating machine part typically results in a force having amplitude proportional to the square of the frequency ω.
(a) Show that the amplitude of the steady periodic solution of the differential equation
(with a forcing term similar to that in Eq. (17)) is given by
(b) Suppose that c2 < 2mk. Show that the maximum amplitude occurs at the frequency ωm given by
Thus the resonance frequency in this case is larger (in contrast with the result of Problem 27) than the natural frequency ω0 = √k/m.
Problem 27
According to Eq. (21), the amplitude of forced steady periodic oscillations for the system mx'' + cx' + kx = F0 cos ωt is given by
Step by Step Answer:
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis