The inclined plane sits on a frictionless plane and m 1 and m 2 are initially at rest. The cylinder rolls down the inclined plane. Find the linear velocity of m 1 and m 2 when m 1 leaves m 2 . 28. Two harmonic oscillators are coupled together by a spring of spring constant k'. Each oscillator has a particle of mass m.
All springs are massless.
The spring constant of one oscillator is k 1 and that of the other is k 2 . The motion of the masses is restricted to a line joining the two masses. Briefly discuss the symmetry of the normal modes. Neglect the effects of gravity. For small oscillations, find the Lagrangian of this system in terms of and the contents given in the diagram above.