A spring is standing upright on a table with its bottom end fastened to a table.

Question

 A spring is standing upright on a table with its bottom end fastened to a table. A block is dropped from a height 3.0cm above the top of the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10cm. What is the oscillation frequency? 

Explanation / Answer

We know that          Workdone = changein PE           F.x = mgh -0          0.5kx.x = mgh          0.5kx2= mgh          ==> k / m = 2gh/ x2                               = 2 * 9.8 *(0.03+0.1) / 0.12                          = 254.8 We know that angular frequency                = k / m                   = 254.8                   = 15.96 rad/sec Therefore oscillation frequency             f = / 2               = 15.96 / 2 * 3.14               = 2.541 Hz

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