Which Spring Oscillation Frequency is Correct?

[JoanF]

Homework Statement

mass of the body=m

Horizontally, the spring is deflected from its equilibrium position and then released, oscillated with a frequency f. Then, the same spring and the same body are suspended vertically, as in figure.

Which one is correct?

A) The frequency of movement of the spring, when the body is suspended vertically, doubled.

B) The frequency of movement of the spring, when the body is suspended vertically, reduced to half.

C) The frequency of movement of the spring, when the body is suspended vertically, remains the same.

D) The frequency of movement of the spring, when the body is suspended vertically, is not related to the period of the movement, when the spring oscillates horizontally.

Homework Equations

The Attempt at a Solution

I think is C) but I think that D) is also correct. Please help me

 

[Doc Al]

Describe how you came to that conclusion.

 

[JoanF]

I think is C) because the frequency is a characteristic of the oscillator.

I think that D) is also correct because we change the position of oscillator and in the second case there are 2 forces: grav force and elastic force, in the first case there is only elastic force.

 

[Doc Al]

It's true that when suspended vertically there are two forces to consider, but it still turns out that the frequency depends only on the ratio of k/m.

How does period relate to frequency?

 

[JoanF]

f= 1/T

so is C) ?

 

[Doc Al]

f= 1/T

Right.

so is C) ?

Yes, C is correct. D doesn't really make sense, since if the frequency is unchanged the period must also be unchanged.

 

[JoanF]

so the in spite of in 2nd case there are 2 forces acting, that doesn't change anything, right?

 

[Doc Al]

so the in spite of in 2nd case there are 2 forces acting, that doesn't change anything, right?

What changes is the length of the spring when the system is at its equilibrium point. In the horizontal case, the equilibrium position is when the spring is unstretched; but when vertical, the spring is stretched at equilibrium (by an amount = mg/k).

But that doesn't affect the choice of answer.

 

[JoanF]

oh ok, now I understand

many thanks, really!