Solving Motion in Springs: A Beginner's Guide

[craigthecraig]

I have no idea where to start with springs,I like to blame my lecturer...
Anyway I have a past paper and there's a question that goes something like this

A particle of mass m hangs freely suspended by a light elastic spring of stiffness k.
In equilibrium, the extension of the spring is d. If x is used to measure the downward displacement of the particle beyond its equilibrium position,show that the equation of motion for the particle is
..
x+(g/d)x=0 t>0 (The first x is x double dot,or acceleration)

where g is acceleration due to gravity.

It seems like a simple enough problem,I just don't know where to begin.Any ideas?

 

[pizzasky]

Start by analyzing the forces acting on the mass when it is in equilibrium. You will get an expression that will be useful later on in the question.

Then analyze the forces acting on the mass when it is pulled a further distance downward beyond equilibrium position. Use Newton's 2nd Law and take note of your sign convention! Is downward or upward the positive direction? Read the question carefully to determine this!