Calculate the equation for laplace transform

Reference no: EM132454998

Problem Statement:

Statement:- The equations of motion for the system shown below (assuming small angle displacements) are given by:
(??1 + ??2)??1
2??¨
1 + ??2??1??2??¨
2 + (??1 + ??2
)??1????1 = 0 1)
??2??2
2??¨
2 + ??2??1??2??¨
1 + ??2??2????2 = 0 2)

Solve the system for exact solutions of ??1 ?????? ??2 via Laplace Transform and numerically approximate the solution for ??1
(3), ??2
(3) using your own 4th

-order RK method and a step size of 0.25 for the ollowing conditions:

??1 = ??2 = 1 ????
??1 = 4 ????, ??2 = 8 ????
??1
(0) = 1°, ??2
(0) = -1°
???
1
(0) = ???
2
(0) = 0°/??
?? = 9.81 ??2
/??

Statement:-Generate a report showing your solution development for both methods. Include plots of the response
for ??1, ??2, ???
1, ???
2, ??¨
1, ?????? ??¨
2 from t = 0-2 sec for both methods (plot both methods on the same graph for each position , velocity, and acceleration). Submit your report (as a pdf) and your Matlab script to BB.

Reference no: EM132454998

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