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zepelin [54]
3 years ago
9

A model of a spring/mass system is 4x'' + e−0.1tx = 0. By inspection of the differential equation only, discuss the behavior of

the system over a long period of time.
Physics
1 answer:
Delicious77 [7]3 years ago
4 0

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 e^{-0.1t} = 0 as t tends to infinity

4x'' + e−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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