# Vertical, spring and frequency

1. Homework Statement

A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the spring is at its rest length. The object is then released from yi and oscillates up and down, with its lowest position being 21 cm below yi.

What is the frequency of the oscillation?

2. Homework Equations

T = 2pi sqrt(m/k)

Analyzing the forces,

At the rest position:
Fnet = k(yi) - mg = o
k(yi) = mg

Maximum distance below the rest position,

Fnet = k($$\Delta$$y)

I know that the total energy of the system is given by the following:

E= U + K = 1/2k(A)^2

3. The Attempt at a Solution

Since I finding frequency I can just take the reciprocal for the equation for period:
f = (1/2pi)*sqrt(k/m)

I don't have any masses given so I'm assuming that I have to find the analytic solution for k that will cancel out the m.

I know that k = (mg/yi) but I wasn't given what yi is.

I'm think I have to do something with the energy of the system.

I really think I need more information, but there must be some way to solve this problem.

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A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest in a position yi such that the spring is at its rest length. The object is then released from yi and oscillates up and down, with its lowest position being 21 cm below yi.

What is the frequency of the oscillation?
The first step is to prove that an oscillating body hanging from a spring executes SHM.

Let a body of mass m hang in equilibrium by stretching the spring by a length of x1. Then,

mg = kx1.

(Edited:)

Now suppose the spring is stretched by a dist x2 from its unstretched length position. Write down the force eqn and prove that it is indeed an SHM. (Consider x=x2-x1.)

After that, you can use all the results of SHM.

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