Find the frequency of vibration and the total glue has dissolved. Two equal mass

Question

Find the frequency of vibration and the total glue has dissolved. Two equal masses of 0.6 kg are glued to each other and connected to a spring of spring constant 240 N/m. The masses, which rest on a horizontal frictionless surface, are displaced 0.600 m from their equilibrium positions and released. Before being released, a few drops of solvent are dropped on to the glue bonding the two masses together. Find the frequency of vibration and the total mechanical energy of the system before glue has dissolved. Find the subsequent frequency of vibration and the energy of the vibrating system if the glue dissolves at maximum compression of the spring.

Explanation / Answer

1) F= w/2pi = 1/2pi * sqroot (k/m) = 1/2pi * sqroot (240/1.2) = 2.25 N

ME= PE = 1/2 KX^2 = 43.2 J

2) X=0 (equilibirium) KE= 1/2KEmax and KEmax=MEtoltal 1/2MEtotal=1/2(43.2)=216J

F=1/2pi sqroot (240.6) = 3,18 Hz

3) mass in the right is released with V=0 so the system energy remains 43.2J F = 3,18Hz

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