How Do You Calculate Frequency and Period for a Mass on a Spring?

[Brownie7]

Waves and Sound Vibrations Question Urgent Please Help??

Homework Statement

A mass suspended from the end of a spring vibrates up and down 25 times in 50s. What ar ethe frequency and period of the vibration.

Homework Equations

F = 1/T
T = 2(pie)3.14(squrroot)L/g

The Attempt at a Solution

F = 1/T
or is it:
F = 50/25
F = 2Hz?

T = 2(3.14)(sqrroot) but what is the L?

I'm very confused and I need to finish this soon!

 

[rl.bhat]

Frequency = number of vibrations per second.
Period T = time for one vibration = 1/f

 

[tomcue]

Based on the given information, we can solve for the frequency and period of the vibration using the equations F = 1/T and T = 2π√(L/g).

First, let's determine the period (T) of the vibration. We know that the mass vibrates 25 times in 50s, so we can write this as a ratio of 25/50. The period is the time it takes for one complete cycle, so we can divide 50s by 25 to get the period of 2s.

Next, we can use the equation T = 2π√(L/g) to solve for L, which represents the length of the spring. We know that g is the acceleration due to gravity (9.8 m/s^2) and we can plug in the period of 2s, so we have:

2s = 2π√(L/9.8 m/s^2)

To solve for L, we can square both sides of the equation to get rid of the square root:

4s^2 = 4π^2(L/9.8 m/s^2)

Now we can multiply both sides by 9.8 m/s^2 and divide by 4π^2 to isolate L:

L = (4s^2)(9.8 m/s^2) / (4π^2)

L = 9.8s^2 / π^2

Finally, we can plug this value of L into the equation F = 1/T to solve for the frequency (F):

F = 1 / (2s)

F = 0.5 Hz

So the frequency of the vibration is 0.5 Hz and the period is 2s. I hope this helps! Remember to always label your units and double check your calculations. Good luck!