f(x) = a*sin(omega*x+c) + d
a               = 0.920921   
omega      = 1.49987     
c               = -1.5708      
d               = -0.0790786
 g=29.3
 df(x) = (x-1)**2*(g**2-1)**2-g**2
 cf(x) = -(g**2-1)*(g-0.5)/g**2
 hf(x) = cf(x)/df(x)
 
 hfenergy(x) = 0.5*(x*g)**2