Find the motion of the mass-spring system in the figure below with mass 0.125 kg damping 0, spring constant 1.125 kg/sec², and driving force cost-4 sint newtons, assuming zero initial displacement and velocity. Calculate the frequency of the driving force that would get you resonance to three decimal places.
Find the motion of the mass-spring system in the figure below with mass 0.125 kg damping 0, spring constant 1.125 kg/sec², and driving force cost-4 sint newtons, assuming zero initial displacement and velocity. Calculate the frequency of the driving force that would get you resonance to three decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find the motion of the mass-spring system in the figure below with mass
0.125 kg damping 0, spring constant 1.125 kg/sec², and driving force
cost-4 sint newtons, assuming zero initial displacement and velocity.
Calculate the frequency of the driving force that would get you resonance to
three decimal places.
Transcribed Image Text:The equation is
thus,
0.125y" + 1.125y = cost - 4 sint;
y" +9y = 8 cos t - 32 sin t.
The solution satisfying the initial conditions is
y = - cos 3t+ sin 3t+cost - 4 sin t,
as obtained by the method of undetermined coefficients.
The last two terms result from the driving force. In the first two terms,
wo = √k/m = 3. This shows that resonance would occur if the driving force had
the frequency w(2T) = 3/(2T).
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