ENGR 202: ENGINEERING ANALYSIS II NUMERICAL INTEGRATION Name: XXXXXXXXXXApril 21, 2022 Consider an elastic pendulum shown in the below figure. The motion of the system is described by the following...

HW


ENGR 202: ENGINEERING ANALYSIS II NUMERICAL INTEGRATION Name: April 21, 2022 Consider an elastic pendulum shown in the below figure. The motion of the system is described by the following two second-order differential equations: 2 + ?? cos ?? − ?? (?? − ??0) ??? = ????? ?? ??? ?? ??? = −2 ??? − sin ?? ?? ?? where ??0 is the unstretched length of the pendulum. Assume ?? = 9.81 m/s2 , ?? = 5 kg, ??0 = 1 m, ?? = 500 N/m. The initial conditions are ??(0) = ??0 , ???(0) = 0, ??(0) = ?? , ???(0) = 2 rad 2 2 s Do the following: 1) Part (1) Solve the initial-value problem numerically using the Euler’s method and the time step ℎ = 0.01 second for ?? = 1,2, … ,10. Present the numerical values of ??, ???, ??, and ??? vs. ?? in a table. 2) Part (2) Write a computer program to numerically solve the initial-value problem using the time step ℎ = 0.01 second and the methods Euler second-order Runge-Kutta Plot each of ??(??), ???(??), ??(??), and ???(??) from the two methods versus ?? for 10 seconds in the same graph. General Rules • Submit a report describing your solution step by step. • The report can be hand-written or typed. • Computer programs can only be included as supplements. No credit will be given if you submit only the computer program.