[ElMoro]

Hiya, I'm a bit rusty with M3 so I'd appreciate if someone could explain where I'm going wrong with these questions

The first question:
A particle of mass 0.4kg is fixed to one end A of a light elastic spring AB, of natural length 0.8m and modulus of elasticity 20N. The other end of B of the spring is attached to a fixed point. The particle hangs in equilibrium. It is then pulled vertically downwards through a distance 0.2m and released from rest. Find the initial acceleration of the particle.

Using Hooke's law, the tension = 5N and resolving forces upwards gives us 0.4a = 5 - 0.4g so a = 2.7ms^(-2) however the answer is 12.5ms^(-2) as if the weight of the particle has been disregarded?

The second question:
A particle of mass 2kg is attached to one end P of a light elastic string. The other end Q of the spring is attached to a fixed point O. The spring has natural length 1.5m and modulus of elasticity 40N. The particle is held at a point which is 1m vertically above O and released from rest. Find the initial acceleration of the particle, stating its magnitude and direction.

Since the spring was compressed, I assumed it was in thrust (not tension). Using Hooke's Law, T=40/3 and resolving forces downwards gives us 2a = 40/3 + 2g so a = 16.5ms^(-2) downwards however the answer is given as 3.13ms^(-2) downwards as though the spring is in tension. I don't understand this.

Thanks for your time

[james22]

The extension isn't 0.2, its 0.2 below equilibrium. Whats the extension at equilibrium?

[Augmented hippo]

Ok, in the first question it is pulled 0.2 me below equilibrium so the weight can kind of be disregarded as the weight balanced with the original extension.
And in the second question the particle is held above O not below as in your sketch.
Hope this helps

[ElMoro]

Thanks guys! I knew I was missing something simple

I ran out of rep, james22, but I'll get to it eventually