Calculating Equilibrium Position of a Spring with a Hanging Mass

[ricoxg]

Question is:

A particle hangs from a spring and oscillates
with a period of 0.4 s.
If the mass-spring system remained at rest,
by how much would the mass stretch it from
its normal equilibrium position? The acceler-
ation of gravity is 9.8 m/s2.

And the choices are:

1. 0.158872 m
2. 0.0794358 m
3. 0.124777 m
4. 0.317743 m
5. 0.0397179 m
6. 0.635486 m

I tried answer #6 but it wasn't right. I used W=SqRt of K/M

 

[rl.bhat]

I used W=SqRt of K/M
In the above equation put the expression for k and solve for x.
You know that
F = Mg = - kx

 

[ricoxg]

how would i solve for k?

 

[rl.bhat]

ω= sqrt(k/m) = sqrt(-mg/xm) = sqrt(-g/x)
Square the both sides and solve for x.