How Do Spring Constants Affect Harmonic Motion Periods and Frequencies?

[amasu]

I am a Swedish exchange student, it is the first time i am on this website and truthfully i am desperate.

I need to know how to solve these 4 basic questions.

Homework Statement

1. A feather is pulled out 4 cm if you hang 50 grams in it. If the spring is then loaded with a total of 150 grams and can pivot up and down the harmonic motion, which is the period?

2. A mass of 0.5 kg undergoing harmonic motion with a frequency of 2 Hz and an amplitude of 8mm. calculate:

a maximum speed of the Mass

b Maximum Acceleration of the mass

c The maximum force of the mass

3. A machine produces a certain distance of the sound level 87 decibels, how big would the noise level be if three such machines started simultaneously next to each other?

4. A string has a fundamental frequency of 294 Hz. then press down your finger on the string and it will be 25% shorter. What is the new frequency for the new basic tone that arise?

Homework Equations

The Attempt at a Solution

I tried to solve the 1st question and this is how far i came:

My solution: I started with Hooke's law

f =-k * x

F =-k * x

-0.05 * 9.82 =-k * 0.04

0.491 = k * 0.04

0.491 / 0.04 =-k * 0.04 / 0.04

k = 0.491 / 0.04

k = -12.275

 

[Simon Bridge]

Welcome to PF;
Lets deal with them one at a time:

1. A feather is pulled out 4 cm if you hang 50 grams in it. If the spring is then loaded with a total of 150 grams and can pivot up and down the harmonic motion, which is the period?

... does this mean that the feather is being modeled as a spring? i.e. if the feather was released, it would retract back completely?

F =-k * x

-0.05 * 9.82 =-k * 0.04

0.491 = k * 0.04

0.491 / 0.04 =-k * 0.04 / 0.04

k = 0.491 / 0.04

k = -12.275

... so far so good, only the mass was 150g. But the question asks for the period.
Do you know the relationship between the period and k?

 

[amasu]

Welcome to PF;
Lets deal with them one at a time: ... does this mean that the feather is being modeled as a spring? i.e. if the feather was released, it would retract back completely?

... so far so good, only the mass was 150g. But the question asks for the period.
Do you know the relationship between the period and k?

FINALLY SOMEONE REPLIED!

Yes, sir it is supposed to be like a "spring", ie. it goes back up.

The relationship between the period and the spring is

T= 2*pi* sqrt(mass/k)

So if the K is correct as you indicated the formula will look like this:

T= 2* pi* sqrt (0,15/12,075)

T= 0,700 seconds

right?

 

[amasu]

Also i tried solving this one:

2. A mass of 0.5 kg undergoing harmonic motion with a frequency of 2 Hz and an amplitude of 8mm. calculate:

a maximum speed of the Mass

b Maximum Acceleration of the mass

In (a) i got the two answers 0,314 meter/seconds and 1,4 meter/seconds (i don't know which of them was right so i wrote down both these solutions)

In b) the accelaration was 0,493 meter/seconds

I am right, yes?

 

[BvU]

Hello Ama,
The way this forum works is you state as best you can the problem, the relevant equations and your attempt to a solution. That way someone can try to help you in a constructive way. You don't benefit from a yes/no answer to your "I am right, yes?" question.
So: please show what you do to come to these (two?) answers. (And the answer to your question is "no").

 

[Simon Bridge]

So if the K is correct as you indicated...

... I don't think I did.
Your value of k was:

k = -12.275

... how can k be negative?
... doesn't k have units?

In your subsequent calculation for the period you did:

T= 2* pi* sqrt (0,15/12,075)

... you used k=12.075 (units?) here, this is different from what you calculated.

You did show your working though.
Unfortunately post #4 tells me nothing about how you approached the problem.
As BvU points out, this makes it difficult to respond.

All I can tell is that your units for acceleration are incorrect.

The way to write these problems well is to assume that we are not going to do any of the working out ourselves and you have to show us that you are getting it right. We don't know the right answer until you calculate it. But we do know the right path to follow to get to the right answer: so show us the path you followed.