A spring/mass/dashpot system has mass 16 kg, damping constant 448 kg/sec and spring constant 5776 kg/sec/sec. Express the ODE for the system in the form x"+2px'+w²x = 0 Identify the natural (undamped) frequency of the spring: (square Hz) wo = Identify the parameter p: P = Now assume that the system has the oscillating forcing function cos(wot) with the same frequency as the spring's natural frequency. Complexify the ODE and use the real part as a particular solution: x"+28x'+361x = cos(wot) Xp (Hz) = (meters)
A spring/mass/dashpot system has mass 16 kg, damping constant 448 kg/sec and spring constant 5776 kg/sec/sec. Express the ODE for the system in the form x"+2px'+w²x = 0 Identify the natural (undamped) frequency of the spring: (square Hz) wo = Identify the parameter p: P = Now assume that the system has the oscillating forcing function cos(wot) with the same frequency as the spring's natural frequency. Complexify the ODE and use the real part as a particular solution: x"+28x'+361x = cos(wot) Xp (Hz) = (meters)
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Transcribed Image Text:A spring/mass/dashpot system has mass 16 kg, damping constant 448 kg/sec and spring constant 5776
kg/sec/sec. Express the ODE for the system in the form
x"+2px'+w²x = 0
Identify the natural (undamped) frequency of the spring:
wo =
Identify the parameter p:
p =
Xp
(square Hz)
Now assume that the system has the oscillating forcing function cos(wot) with the same frequency as the
spring's natural frequency. Complexify the ODE and use the real part as a particular solution:
x"+28x'+361x = cos(wot)
=
(Hz)
(meters)
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