Given, height, h=1m mass, m=1kg spring constant, k=15Nm−1 The kinetic energy of mass after falling on the platform will be converted into potential energy of the spring. Thus, mg(h+x)=
1
2
kx2 1×10(1+x)=
1
2
×15×x2 ⇒10×
2
15
(1+x)=x2 ⇒
4
3
(1+x)=x2 ⇒4+4x=3x2 ⇒3x2−4x−4=0 ⇒3x2−6x+2x−4=0 ⇒3x(x−2)+2(x−2)=0 ⇒(x−2)=0 or (3x+2)=0 x=2m or x=
−2
3
m Since, x is the compression, which cannot be negative, thus x=2m.