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.

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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.

Physics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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.
@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 ?

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

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