Solid cylinder of mass m is connected to the two springs of total stiffness k as shown. Each of the springs is attached to a wall. Find the period of small oscillations of the cylinder assuming that it does not slide on the floor.

Question

anonymous · Answer

here is the pic attached

vincent-lyon.fr · Answer

Your system is conservative since the cylinder is not slipping.
Use energy method, choosing a common parameter such as the position of the centre of the cylinder x and its derivative v.

Kinetic Energy =    .......    +    .........  = f(v)
Elastic potential Energy = .........  +  .......... = g(x)


Sum is constant, so add them up and take time-derivative.

anonymous · Answer

@vincent  in above problem if we have frictional force in addition then it will be non conservative force system 
then how are we gonna solve this problem ?

vincent-lyon.fr · Answer

You can use the same method, slighly adapted for your new situation.

The derivative of total energy is not 0, but is equal to the (negative) power of the friction force.

anonymous · Answer

ooh I see so you are still taking sum of total forces (conservative+ non cons) eqauls to zero am I right? @Vincent-Lyon.Fr