What physics is involved in a swinging spring?

[Haydos]

I have this physics assignment where i have to build a home made accelerometer out of a spring and a cork. i have to relate acceleration and the angle of deflection (a = tan angle). Furthermore i have to explain why their is in angle of deflection in the spring. I know when springs compress and contract they follow hooke's law. however the spring in this experiment is moving side to side. What principles does a spring moving side to side follow? Thanks in advance