Matlab has a function ode45 for solving initial value problems for ordinary differential equations. This function implements a RungeKutta method with a variable time step for efficient computation. 
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Topic 
Script 
Free vibration of a singledegreeoffreedom system. 
free_ode45.m

Free vibration of a coupled, multidegreeoffreedom system.  mdof_ode45.m MDOF_simulation.m Generalized_Eigen.m matlab_ODE45_MDOF.pdf ODE45_matlab_tutorial.pdf 
Free Vibration of a Singledegreeoffreedom System with Nonlinear Stiffness. 
nonlin.pdf sdof_stiff2_ode45.m sdof_stiff2_free_function.m 
Free vibration of a pendulum. This program solves the nonlinear equation of motion such that large angular displacements are allowed. 
pendulum_free_ode45.m pendulum_free_function.m 
Vibration of a singledegreeoffreedom system subjected to sinusoidal base excitation. 
sinebase_ode45.m sinebase_function.m bode_transfer_function.m 
Vibration of a singledegreeoffreedom system subjected to arbitrary base excitation. The script takes an FFT of the input excitation. The FFT parameters are then passed to the supporting function which reconstructs the time history. 
arb_base_ode45.m 
Vibration of a singledegreeoffreedom system subjected to sinusoidal force excitation. 
sineforce_ode45.m

See also: Matlab Matlab_Newmark_PageMatlab RK4 Page 

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