Find the equation of motion using the Energy method. PE + KE Solution In the above system, If the vertical string moves by x, The horizontal will move by x/2 because it is on the smaller radius disc. By conservation of energy method; PE = 0.5(k)(x/2)^2 +0.5(2k)(x)^2-2mgx KE = 0.5(m)(v/2)^2 + 0.5(Id)(wd)^2 + 0.5(Ip)(wp)^2+(0.5)(2m)(v)^2 relating friction less slipping; wd = v/2rd ; rpwp = v/2 Now using these relation ships; differentiate w.r.t time. So d/dt (P.E +K.E) = 0 Use x(dot) = v and x(double dot) = a. to get the equations of motion. Since time is only 2 mn left before expiry. I couldn\'t give the differentiated explanation.

1. Find the equation of motion using the Energy method. PE + KE
Solution
In the above system, If the vertical string moves by x, The horizontal will move by x/2 because it
is on the smaller radius disc.
By conservation of energy method;
PE = 0.5(k)(x/2)^2 +0.5(2k)(x)^2-2mgx
KE = 0.5(m)(v/2)^2 + 0.5(Id)(wd)^2 + 0.5(Ip)(wp)^2+(0.5)(2m)(v)^2
relating friction less slipping;
wd = v/2rd ; rpwp = v/2
Now using these relation ships; differentiate w.r.t time.
So d/dt (P.E +K.E) = 0
Use x(dot) = v and x(double dot) = a. to get the equations of motion.
Since time is only 2 mn left before expiry. I couldn't give the differentiated explanation