plz send the python scripts and result （graphs）. Thx
Posted: Tue Apr 26, 2022 7:07 pm
plz send the python scripts and result （graphs）.
Thx
1 Nonlinear pendulum (50 points) For a frictionless pendulum, the motion of the pendulum is d-0 dt I sino (1) L For this problem, use g = 4, L = 1 and m = 1. Here g is the gravitational acceleration, L is the length of a massless cord that supports the mass m. And we have initial conditions e(t = 0) = 0, which will be specified below and w(t = 0) = 0.w = ili is the angular velocity. de dt
1. a For small initial angle 0 <1 (0 is in radians), the equation can be simplified to de dt? 290 (2) L Then for this linear differential equation, the solution is well-known. It is cos(2#t/Ti). Ti = 25L/g is the period in this linear approximation. For o 0.7, use the second-order Runge-Kutta method plot the solution and the linear approximation in the same graph. Use 100 time steps, from t = 0 to t = 57.
1. b Because the total energy of this frictionless pendulum should be strictly zero, the error can be seen more clearly from the total energy. For the nonlinear pendulum, the total energy is the sum of the potential energy mgl (costo – cos8) and the kinetic energy ml?w2. For 10 1, use 100 time steps, for time from t = 0 to t = 57. Plot the total energy as a function of time for both the second-order Runge-Kutta method and the fourth-order Runge-Kutta method. Since their magnitudes are quite different, plot them in separate graphs.
Thx
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1. a For small initial angle 0 <1 (0 is in radians), the equation can be simplified to de dt? 290 (2) L Then for this linear differential equation, the solution is well-known. It is cos(2#t/Ti). Ti = 25L/g is the period in this linear approximation. For o 0.7, use the second-order Runge-Kutta method plot the solution and the linear approximation in the same graph. Use 100 time steps, from t = 0 to t = 57.
1. b Because the total energy of this frictionless pendulum should be strictly zero, the error can be seen more clearly from the total energy. For the nonlinear pendulum, the total energy is the sum of the potential energy mgl (costo – cos8) and the kinetic energy ml?w2. For 10 1, use 100 time steps, for time from t = 0 to t = 57. Plot the total energy as a function of time for both the second-order Runge-Kutta method and the fourth-order Runge-Kutta method. Since their magnitudes are quite different, plot them in separate graphs.