The slider crank mechanism is given in the vertical plane as shown below. The load
F(t)
is applied to point
B
that is always parallel
BC
link. The torsional spring stiffness at point
A
is
k
, and it is in equilibrium when
\theta =60\deg
. The links
AB
and
BC
are same, their masses are
m
. The collar
C
mass is negligible. a) Find the equation of motion
(\theta ^(¨))
for the system in terms of
\theta
and
\theta ^(?)
by using Newton's Laws. pts) b) Find the equation of motion
(\theta ^(¨))
for the system in terms of
\theta
and
\theta ^(?)
by using Energy Method. pts) Bonus Part : (25 pts) Plot the linear position and velocity of point
C
for 2 second, when
g=9.81(m)/(sec^(2),l)=200mm,m=1kg,\theta _(0)=60\deg ,d(\theta _(0))/(d)t=0.5ra(d)/(sec,F)=0
and
k=0
.