Simple Harmonic Motion:Physics

Question

A spiral spring was displaced 5cm vertically down when a load of 25N was attached to it. Find the maximum displacement produced when a mass of 0.6kg was dropped into the attached scale pan from a height of 10cm.

Answer 1

First find the spring constant using the data. F=kx where F=25N and x=.05 m so k= 500 N/m> Now setup the following equation mg(h+x)= kx²/2 Using the data .6(9.8)(.1+x) =250 x² so .588+5.88 x =250x² rearranging the terms 250x² -5.88x -.588 =0 and x² -.023x -.0023 =0 using the quadratic formula gives x= 6.1cm.