Question

Create a Matlab code to solve the two following equations for a pendulum:

F = 10

m = 1

ks = 1

(m+M)x'' - ml$\Theta$'' cos$\Theta$ + ml$\Theta$'' sin$\Theta$ = F

-x'' cos$\Theta$ + l$\Theta$'' - g sin$\Theta$ = 0

Answer 1

function T- pendulum(L, a0) %PENDULUM Summary of this function goes here % Detailed explanation goes here %initializing variables alpha a0; delta t-1*10-6; g= 9.8; stop - false; theta- a0 omegalast-0 %Set stop falsE so that loop stop isn't true at start while stop false: %increment t for each step into loop t- t+ delta t; %compute alpha using given formula alpha--g/L*sin(theta); %compute omega as alpha times timestep, delta t omega = alpha*delta t: %theta is then theta plus omega times delta t theta- theta + omega*delta t %check to see if pendulum speed has %slowed down from the last timestep %This indicatest that pendulum is now past the %minimum point so stop program if abs(omega) <abs(omegalast) stop true

en %IF THE SOFTWARE SHOULD STOP IT IS NOW SET TO DO SO %SET OMEGALAST EQUAL TO OMEGA FOR CHECK IN NEXT TIME STEP omegalast-omega: en %COMPUTE PERIOD AS 4 TMES ELAPSED TIME TO BOTTOM OF PENDULUM T = 4 *t; en