# Modfied pendulum equation ch1-pendulum.ode 

# This script simulates a modified version of the pendulum equation x'' + sin(x) = 0 in which 

# friction is included and we allow the pendulum pin to be vibrated vertically.  

# (See Chapter 1 Exercises in the textbook.)  There are three parameters:  beta (the friction coefficient),

# alpha (proportional to amplitude of vibration) and omega (frequency of vibration).  The variable x is the

# angle relative to the downward vertical position, and y = x'.

dx/dt=y

dy/dt=-beta*y-(1.0+alpha*omega^2*cos(omega*t))*sin(x)



# Set the default value of the parameters:

# Don't put spaces between the parameter name, the equal sign, and the parameter value!

par beta=0.05,alpha=0.1,omega=0.5



# Set the default initial conditions:

init x=3.1  y=0.0



# Set the axes to plot displacement x versus time t: 

@ xplot=t, yplot=x



# Set the maximum number of data points to store, stopping time, time step, and default viewing window
@ maxstor=50000,total=200,dt=.005,xlo=0,xhi=200,ylo=-2.0,yhi=2.0


done