A mass weighing 8 lb stretches a spring 1 ft, and it is attached to a dashpot me
ID: 3163567 • Letter: A
Question
A mass weighing 8 lb stretches a spring 1 ft, and it is attached to a dashpot mechanism that has a damping constant of 2 lb ·s / ft. The mass is set in motion from its equilibrium position with an initial downward velocity of 6 ft/s, and is moreover acted on by an external force of 20 cos 8t lb. Recall that the gravitational constant is 32 ft / s 2 . Find the displacement u as a function of time. What is the natural frequency and the phase of the steady state solution?
the answers are natural frequency of the steady state solution: 8 and the phase of the steady state solution: arc tan(-2)
can you explain how to get two values
u(t) =-e-4tcos(4t)-- ) + sin (8t) cos(St 1-2 1-2Explanation / Answer
Steady state solution from above solution is
Up(t)=(-1/2)cos(8t)+sin(8t)
natural frequency is highlighted in steady state solution equation
W=8 rad/sec
phase
phi=tan-1(1/(-1/2))=tan-1(-2)
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