Simple Harmonic Motion: Mass on a Spring Homework Solution

[bmb2009]

Homework Statement

A massless spring hangs down from a support, with its lower end at y=0, where the y-axis is vertical and points downward (normal orientation of y). When a small unknown mass is attached to the spring, the lower end of the spring moves down to a position y_0 for the mass being in equilibrium

a.) Demonstrate that when the mass is pulled down to a position of y=y_0 + A and released from rest, it will execute a simple harmonic motion around y_0

b.) Express the period of oscillations of the mass in terms of y_0 and g.

Homework Equations

The Attempt at a Solution

Not really sure what/how to demonstrate that it executes s.h.m. I set up a force equation such that F_net= F_restoring - mg

F_net= -k(y-y_0) - mg
let Y be acceleration
mY= -k(y-y_0) - mg

mY=-kA-mg definfe ω^2 = k/m

Y=-(ω^2)A - g is the final equation i got... not sure how this proves anything and not really sure what to do.. any help? thanks

 

[Simon Bridge]

a.) Demonstrate that when the mass is pulled down to a position of y=y_0 + A and released from rest, it will execute a simple harmonic motion around y_0

b.) Express the period of oscillations of the mass in terms of y_0 and g.

Not really sure what/how to demonstrate that it executes s.h.m.

Start with the definition of SHM.

I set up a force equation such that F_net= F_restoring - mg

F_net= -k(y-y_0) - mg

Good start - how is the force related to displacement? Use words - and relate it to the definition of SHM.