Consider the mass-spring system, with mass m in units of slugs, a damping coefficient of 0.50 lb-s/ft,
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Consider the mass-spring system, with mass m in units of slugs, a damping coefficient of 0.50 lb-s/ft, and driven by a periodic external force, 3cos(2t) lb.
my"(t) + 0.50y (t) + ky(t) = 3 cos(2t).
(a) If a mass weighing 8lb stretches the spring 6 inches, determine the model's spring constant k in units of lb/ft.
(b) Using the value of k determined in (a) and leaving m as an unspecified parameter, use undetermined coefficients to find the forced (steady-state) solution in the form
y p (t) = c 1 cos(2t) + c 2 sin(2t). The results for c 1 and c 2 will be expressed as functions of the mass M.
(c) From the result in (b), determine the mass m for which the amplitude of the steady-state response is maximum.
Related Book For
Fundamentals of Electric Circuits
ISBN: 9780073301150
3rd edition
Authors: Matthew Sadiku, Charles Alexander
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