A mass of 20 grams stretches a spring 5cm. Suppose that the mass is also attached...

A mass of 20 grams stretches a spring 5cm. Suppose that the mass is also attached to a damper with constant coefficient 0.4 N·s/m. Initially the mass is pulled down an additional 2cm and released. Write a differential equation for the position u(t) of the mass at time t (make the units meters, kilograms, Newtons, seconds). Do NOT solve the differential equation.

The solution to a differential equation that models a vibrating spring is u(t) = 4e−t cos(3t) + 3e−t sin(3t) + 51 cos(2t) + 25 sin(2t) .

(b) Determine the transient part of the solution.
(c) Determine the phase, quasi-amplitude, quasi-frequency, quasi-period. (d) Determine the steady state part of the solution.
(e) Determine the phase, amplitude, frequency, period. of the steady part of the solution.

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genius_generous answered 1 year ago

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