# Example 18.1
MKS(J)
mb = 6 kg
md = 10 kg
mc = 12 kg
rd = 0.1 m
vb = 0.8 m/s
omd = vb / rd
ve = 0.8 m/s
re = 0.2 m
omc = ve / re
te = 0.5 * mb * vb^2
id = 0.5 * md * rd^2
td = 0.5 * id * omd^2
ig = 0.5 * mc * rd^2
vg = 0.4 m/s
tc = 0.5 * mc * vg^2 + 0.5 * ig * omc^2
te + td + tc

# Example 18.2
MKS(N, J)
m0 = 10 kg
M0 = 50 N m
p = 80 N
h = 1.5 m
uw = m0 * grav() * h
delq = pi() rad / 2
um = M0 * delq
k = 30 N/m
us = -0.5 * k * ((2.25 m)^2 - (0.25 m)^2)
up = p * pi() / 2 * 3 m
u = uw + um + us + up

# Example 18.3
MKS(N, J)
m0 = 30 kg
om = 20 rad/s
f = 10 N
M0 = 5 N m
r = 0.2 m
io = 0.5 * m0 * r^2
T2 = 0.5 * io * om^2
q = T2 / (M0 + f * r); rad; rev

# Example 18.4
MKS
m0 = 700 kg
q = 30 deg
x = 0.4 m
r = 0.15 m
ig = 0.5 * m0 * r^2
begin
  om = 1 rad/s
  dely = x* (1 -  cos(q))
   up  = m0 * grav() * dely
  vg = x * om
  t2 = 0.5 * m0 * vg^2 + 0.5 * ig * om^2
   e = up - t2
end
solve(e, om)
begin
   alp = 1 rad/s^2
   ft0 = 1 N
   nt = 1 N
   ag = alp * r
   fx = ft0 - m0 * ag
   fy = nt - m0 * grav() - m0 * om^2 * x
   MM = (m0 * r^2 + m0 * x^2) * alp
end
solve(fx,fy,MM,alp,ft0,nt)

# Example 18.5
FPs
w0 = 40 lb
m0 = w0 / grav()
rg = 0.6 ft
ig = m0 * rg^2
M0 = 15 lb ft
delx = 0.5 ft
k = 10 lb/ft
begin
  om = 1 rad/s
   vg = 0.8 ft * om
  t2 = 0.5 * m0 * vg^2 + 0.5 * ig * om^2
   delq = 0.625 rad
   delx = 1 ft
   um = M0 * delq
   uk = 0.5 * k * delx^2
  e = t2 - um - uk
end
solve(e, om)

# Example 18.6
MKS(N, J)
m0 = 10 kg
p = 50 N
q = 45 deg
x = 0.8 m
rg = (x/2) * tan(q)
ig = (1/12) * m0 * x^2
begin
  om = 1 rad/s
  vg = rg * om
  t2 = 0.5 * m0 * vg^2 + 0.5 * ig * om^2
  up = m0 * grav() * (x/2) * (1 - cos(q)) + p * x * sin(q)
  e = t2 - up
end
solve(e, om)

# Example 18.7
MKS(N, J)
m0 = 10 kg
k = 800 N/m
q = 30 deg
x = 0.4 m
y1 = (x/2) * sin(q)
s1 = x * sin(q)
v1 = -m0 * grav() * y1 + 0.5 * k * s1^2
ig = (1/12) * m0 * x^2
begin
  om = 1 rad/s
  vg = (x/2) * om
   t2 = 0.5 * m0 * vg^2 + 0.5 * ig * om^2
  e = v1 - t2
end
solve(e, om)

# Example 18.8
w0 = 30 lb
m0 = w0 / grav()
rg = 0.6 ft
ig = 0.5 * m0 * rg^2
k = 2 lb/ft
x0 = 1 ft
delx  = 3 ft
s1 = sqrt(delx^2 + (x0 + delx)^2) - x0; ft
s2 = s1 - x0; ft
v1 = 0.5 * k * s1^2
v2 = 0.5 * k * s2^2
begin
  om = 1 rad/s
  vg = 0.75 ft * om
  t2 = 0.5 * m0 * vg^2 + 0.5 * ig * om^2
  e = t2 + v2 - v1
end
solve(e, om)

# Example 18.9
MKS
m0 = 10 kg
m1 = 5 kg
q = 60 deg
x = 0.6 m
y1 = (x/2) * sin(q)
v1 = m1 * grav() * y1
ig = (1/12) * m1 * x^2
begin
   om = 1 rad/s
   vg = (x/2) * om
   t2 = 0.5 * m0 * vg^2 + 0.5 * ig * om^2 
   e = t2 - v1
end
solve(e,om)

# Homework Problems:

TBD