Vertical, spring and frequency

[ThePhoenixEffec]

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?

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

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.

 

[Shooting Star]

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.

 

[Moetasim]

You are correct in thinking that you need more information to solve this problem. In order to find the frequency of the oscillation, you need to know the mass of the object and the spring constant (k). You can use the equation T = 2pi sqrt(m/k) to find the period of the oscillation, and then use the relationship between frequency (f) and period (T) which is f = 1/T to find the frequency.

Additionally, you can use the information given about the object's maximum distance below the rest position to find the amplitude (A) of the oscillation, which is equal to half of the total distance traveled. Then, you can use the equation E = 1/2k(A)^2 to find the energy of the system, which will also require knowing the spring constant.

In summary, to find the frequency of the oscillation, you will need to know the mass of the object, the spring constant, and the amplitude of the oscillation. Without this information, it is not possible to solve the problem.