# Hanging of Unknown Mass on a spring

## Homework Statement

When a mass is hung from a spring, the spring elongates by 8.2cm. What will the period of the resulting oscillations be if the mass is displaced from equilibrium?

x = 8.2cm OR 0.082m

## Homework Equations

Honestly, i don't have nor do i know of any equations to use for this. I feel like i have zero information here.

## The Attempt at a Solution

?????
Help.

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gneill
Mentor
What is the equation related to the displacement of a spring?

What is the equation for the period of a spring-mass oscillator?

See? You did know something!

The equation for displacement of a string is:
x = Acos(ωt)

as for the period, it's just the time it take for oscillation, i didn't think there was an actual equation for it

You know the eq'n T=2(pi)$$\sqrt{m/k}$$

Now, use Newtons 2nd law to find the answer.

How can i use newton's second law if i don't know the mass, acceleration, or the force? All i have is the length of the spring, and two equations but nothing to fill in for them.

gneill
Mentor
How can i use newton's second law if i don't know the mass, acceleration, or the force? All i have is the length of the spring, and two equations but nothing to fill in for them.
The nice thing about variables is that you don't have to fill any of them in until the very end!

I'm still not getting it, i don't see how i can get an answer out of what i have there. It's just not clicking

gneill
Mentor
I'm still not getting it, i don't see how i can get an answer out of what i have there. It's just not clicking
You hang a mass M on a spring (no oscillations yet!). What's the formula for the displacement of the spring?

tiny-tim
Homework Helper
Hi Hypnos_16! When a mass is hung from a spring, the spring elongates by 8.2cm.
Take questions like this step by step.

What is the equation for this part of the question (static equilibrium)? When a weight is attached and it's in static equilibrium x(length it stretch) = mg / k...if i remember correctly

tiny-tim
Homework Helper
don't "remember" …

work it out!

what are the two equations that govern this situation?

The equations are x = mg / k
and F = kx.

tiny-tim
Homework Helper
The equations are x = mg / k
and F = kx.
hmm The equations are F = mg
and F = kx.

So mg = kx (ie, your memory was correct! ).

ok, now you know g and you know x …

so what can you find? hmm The equations are F = mg
and F = kx.

So mg = kx (ie, your memory was correct! ).

ok, now you know g and you know x …

so what can you find? m/k!!! :)

tiny-tim
Yup! soooo … ? 