A spring/mass/dashpot system has mass 9 kg, damping constant 288 kg/sec and spring constant 3249 kg/sec/sec. Express the ODE for the system in the form I"+2px'+wr=0 Identify the natural (undamped) frequency of the spring: (square Hz) = ولا Identify the parameter p: p= (Hz)
A spring/mass/dashpot system has mass 9 kg, damping constant 288 kg/sec and spring constant 3249 kg/sec/sec. Express the ODE for the system in the form I"+2px'+wr=0 Identify the natural (undamped) frequency of the spring: (square Hz) = ولا Identify the parameter p: p= (Hz)
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Transcribed Image Text:A spring/mass/dashpot system has mass 9 kg, damping constant 288 kg/sec and spring constant 3249
kg/sec/sec. Express the ODE for the system in the form
x"+2px'+wx = 0
Identify the natural (undamped) frequency of the spring:
(square Hz)
wo =
Identify the parameter p:
p=
(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"+32x+361x = cos(wot)
Xp=
(meters)
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