What is the Correct Equation for Calculating the Length of a Spring?

[dinhjeffrey]

Homework Statement

http://img26.imageshack.us/i/1113001.jpg/

#12

Homework Equations

u=(1/2)kx^2
F=mg

The Attempt at a Solution

mg=(1/2)kx^2
√(2mg/k) = x

however, this is not any of the choices.
the correct answer is B)mg/k

 

[Doc Al]

mg=(1/2)kx^2

You seem to be setting a force equal to an energy. Not good.

What's the frequency of a mass on a spring? Of a simple pendulum? Compare.

 

[dinhjeffrey]

okay i got the frequency of a mass of a spring is
f=√(g/L)/2π
and of a simple pendulum
w=√(k/m)

if i set them equal to each other i get
L = mg/(2πk) which is almost right, but the 2π is disregarded in the answer. does anyone know why?

 

[Doc Al]

ω is the angular frequency, not the frequency. To get f from ω, divide by 2pi.