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.

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 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

first thing first of the answer is with technology. second thing second thing is that the big bang theory did not happened u see they say it did but what they dont realize is that like dinasures are still a round they might deny it but they and look at these 12 foot human skelteons they find lets see didnt the bible say something about giants. hope this peace.

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s