2. Consider an unforced spring-mass system whose displacement is modelled by the ODE m x(t)" + cx'(t) + kx(t) = 0, %3! with t in seconds, m = 2 kilograms, k = 5 newtons per meter, and c in N. sec per meter. a) What is the natural frequency of this system, in hertz? b) Find the value of c for critical damping. c) Find the value of c for which the system would oscillate with pseudo-frequency 0.25 hertz. Give the general solution in this case.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Consider an unforced spring-mass system whose displacement is modelled by the ODE
mx(t)" + cx'(t) + k x(t) = 0,
with t in seconds, m = 2 kilograms, k = 5 newtons per meter, and c in N. sec per meter.
a) What is the natural frequency of this system, in hertz?
b) Find the value of c for critical damping.
c) Find the value of c for which the system would oscillate with pseudo-frequency 0.25 hertz.
Give the general solution in this case.
Transcribed Image Text:2. Consider an unforced spring-mass system whose displacement is modelled by the ODE mx(t)" + cx'(t) + k x(t) = 0, with t in seconds, m = 2 kilograms, k = 5 newtons per meter, and c in N. sec per meter. a) What is the natural frequency of this system, in hertz? b) Find the value of c for critical damping. c) Find the value of c for which the system would oscillate with pseudo-frequency 0.25 hertz. Give the general solution in this case.
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