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A model of a spring/mass system is 4x'' + eāˆ’0.1tx = 0. By inspection of the differential equation only, discuss the behavior of the system over a long period of time.

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opudodennis

Answer:

Displacement becomes constant

Explanation:

We know that exponential raised to power infinity (when time is long) equals to zero hence the model system will be [tex]e^{-0.1t} = 0[/tex] as t tends to infinity

4x'' + eāˆ’0.1tx = 0

When t tends to infinity

4x'' = 0

Integrating the above equation we get

4x'=c

Integrating it another time we get

4x=cx+d

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