3a)  with gamma = 0, c = 0, the equation becomes: mL * theta'' + mg * sin(theta) = 0,

so theta'' + g/L * sin(theta) = 0, where g/L = omega^2, for omega = fundamental frequency.

3b)  

Using forward euler's method, I applied it to this problem by rewriting the 2nd order ODE as a
system of 1st order ODE's.

 d/dt [ theta, y ] = f( [ theta , y ] , t)

where y = d(theta)/dt

So:
  z_{n+1} = z_n + dt*f(z_n,t_n)
or
  theta_{n+1} = theta_n + dt*y_n
  y_{n+1} = y_n + dt*{ -c/m*y_n - g/L*sin(theta_n) + gamma cos(omega*t_n) }

  
3c) graph of refinement study is refinementC.ps

3d) graph of refinement study given in refinementD.ps

In both cases, the convergence was O(h^2).