A speing with spring constant $\backslash ($ k $\backslash ),$ free lengthlo certing from ane end and then released by attaching a small top with moss $\backslash ($ m $\backslash )$ to the ether end. The fipure on the side shows the equilibrium state when the spring is free lleft$),$ when a mass $\backslash ($ m $\backslash )$ top is atfachal to the end of the spring $($eenter$)$ ond the situation in both selection and oscillation $($ryant$),$ a$)$ If the boll is assumed to oscilate up and down around its equilurium position in the vertical direction, you solve the equations of mation of the object eceording to the rexistence of the ballin the equilbrum state using Newtoian motron var$$ables$.($showing each propreming

step by step.

b$)$ If the top is apened and released vertially the block oscillates both in the direction of the trection and in the direction of the direction. If this motron is assumed to remain within the verticel plane, write the equations of notion of the obsect usine the Lagrange method $($Showing each prog cormming step.$)$