Period of Oscillation for vertical spring

[conniebear14]

Homework Statement

A mass m=.25 kg is suspended from an ideal Hooke's law spring which has a spring constant k=10 N/m. If the mass moves up and down in the Earth's gravitational field near Earth's surface find period of oscillation.

Homework Equations

T=1/f period equals one over frequency
T= 2pi/w two pi/angular velocity
f=w/2pi
w= (k/m)^1/2
T=2pi/sqrt(k/m)

The Attempt at a Solution

Using these equations I found periods for springs that were horizontally gliding, my question is can I use these same formulas for a vertical spring? Does gravity have to be taken into account?

 

[haruspex]

Does gravity have to be taken into account?

Yes. Since it partly offsets the tension in the spring, it could affect the period. But I'm not asserting that it does. Think about where the mid point of the oscillation will be in terms of spring extension.

 

[conniebear14]

Okay, for this problem let's not take gravity into account. Are my equations correct? Can I use the same approach that I used for a horizontal spring?

 

[haruspex]

Okay, for this problem let's not take gravity into account.

I don't understand. I thought I just advised you to take gravity into account. Just write down the equation for ƩF=ma.

 

[Nickie]

Yes, you can use the same equations for a vertical spring. The only difference is that in a vertical spring, the force of gravity will also play a role in the oscillation. This will affect the equilibrium position and the amplitude of the oscillation, but it will not affect the period of oscillation. The period of oscillation is determined by the mass of the object and the stiffness of the spring, which are the same in both horizontal and vertical situations. Therefore, the period of oscillation for a vertical spring will be the same as the period for a horizontal spring with the same mass and spring constant.