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two balls with masses 1 kg and 2 kg are slipped on a thin smooth horizontal rod. the balls are interconnceted by a light spring of stiffness k=24.the left hand ball is imparted velocity v1=12cm/s.
find the oscillation frequency of the system in the process of motion......???????????
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2 Answers
19vcm = m1v0 / m1 + m2
k.e. of the centre of mass = K=1/2 (m1 + m2 ) vcm2
energy of the 2 blocks is E= 1/2 m1v02
mathematically we see that E>KCM..this difference is the energy of vibration !
thus EVIB = E - KCM
at maximum compression of the spring the whole of the vibrational energy is the elastic potential energy of the spring
=> 1/2 k xm2 = EVIB => xm = √2 EVIB /K
...now its a cakewalk !