First, obtain the set of data of the total mechanical energy $($E $)$ versus time by numerically

simulating the governing equations of motion using ode$23$ to determine the response, $()$ and

$(),$ of the coupled system.

$$ Complete the m$-$file dudt$\_$tmd$($part$)$ based on Eq$.(11).$ Most of that file has already been

completed. For example, the following line of code is the third equation of Eq$.(11).$

udot$(3)=($c$*$u$(4).*$cos$($u$(2))-$ L$*$k$*$u$(1)...$

$+$ L$^2*$m$*$u$(4).^2.*$sin$($u$(2))+$ L$*$g$*$m$*$cos$($u$(2)).*$sin$($u$(2)))...$

$/($L$*($M $+$ m $-$ m$*$cos$($u$(2)).^2))$;

Remember to remove the $($part$)$ from the file name before execution.

$$ In the sample code file, finish typing the lines of code for the definition of the energy

function to obtain the data for the energy based on Eq$.(2).$

$$ Execute the sample code and part $($a$)$ is basically done.