Motion System
Motion System
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Wave Motion - What is the steady state amplitude of the system?
A 45 kg block on a horizontal frictionless surface is connected to a 17 N/m spring. It experiences a forcing function of 25 N Sin(1.5t). What is the steady state amplitude of the system?
45x'' + 17x = 25 * sin(1.5t)
x'' + 17/45 * x = 25/45 * sin(1.5t)
The general solution is:
x = A * cos(1.5t) + B * sin(1.5t)
So:
x' = -A * 1.5 * sin(1.5t) + B * 1.5 * cos(1.5t)
x'' = -A * 2.25 * cos(1.5t) - B * 2.25 * sin(1.5t)
-A * 2.25 * cos(1.5t) - B * 2.25 * sin(1.5t) = 25/45 * sin(1.5t)
This gives: A = 0; B = -25/45 * 1/2.25 = -0.25
Plugging this back into our general solution for x:
x = -0.25 * sin(1.5t)
So our steady state amplitude is |-0.25| = 0.25 m
Hope that helps.


US $29.99












































































