In this problem, you will derive the expression for the average power delivered by a driving force
Question:
In this problem, you will derive the expression for the average power delivered by a driving force to a driven oscillator (Figure).
(a) Show that the instantaneous power input of the driving force is given by
P = Fv AώF0 cos wt sin (ώt – 1).
(b) Use the trigonometric identity sin (θ1 – θ1) = sin θ1 cos θ2 – cos θ1 sin θ2 to show that the equation in (a) can be written P = AώF0 sin δ cos2 ώt – AώF0 cos d cos wt sin ώt.
(c) Show that the average value of the second term in your result for (b) over one or more periods is zero and that therefore.
(d) From Equation 14-50 for tan δ, construct a right triangle in which the side opposite the angle d is bώ and the side adjacent is m(ώ20 – ώ2), and use this triangle to show that
(e) Use your result for (d) to eliminate ώA so that the average power input can be written
Step by Step Answer:
Fundamentals of Ethics for Scientists and Engineers
ISBN: 978-0195134889
1st Edition
Authors: Edmund G. Seebauer, Robert L. Barry