# Homework Help: Natural frequency

1. Sep 17, 2015

### mrblanco

1. The problem statement, all variables and given/known data

Find the natural frequency
2. Relevant equations

On picture
3. The attempt at a solution
Just need help with the equation of motion.

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2. Sep 17, 2015

### Staff: Mentor

Welcome to the PF.

So what are your initial equations? What does the harmonic motion of the block look like, and how is it affected by the part with the levers?

3. Sep 17, 2015

### mrblanco

This is all the information I was given. The block is moving to the left but no values are given. The middle lever has a pin connection

4. Sep 17, 2015

### Staff: Mentor

Well if you only had the spring on the right connected to the block, how would you calculate the resonant frequency?

5. Sep 17, 2015

### mrblanco

Also, I know I have to use rF1+/-rF2=I(alpha) just not sure how

6. Sep 17, 2015

### Staff: Mentor

Where does that come from? Why do you think it is a way to get to the natural frequency of this block/lever/spring system?

7. Sep 17, 2015

### mrblanco

I'm thinking that has to be part of the equation of motion for the block

8. Sep 17, 2015

### mrblanco

If I only considered the spring on the right, I get a complex answer...

9. Sep 17, 2015

### Staff: Mentor

I'll ask again -- what is the resonant frequency of just a single block and spring? -- EDIT -- I see you added that.

And then, what is the action of the lever and the lower spring? Does that force oppose or add to the motion of the block? What do the two sides of the vertical bar (on either side of the fulcrum) do to the level of the 2nd spring's force as applied to the block?

10. Sep 17, 2015

### Staff: Mentor

11. Sep 17, 2015

### mrblanco

12. Sep 17, 2015

### Staff: Mentor

I believe the function of the vertical lever is like a lever arm -- it gives mechanical advantage. What significance does the ratio of a and b have?

13. Sep 17, 2015

### mrblanco

14. Sep 17, 2015

### Staff: Mentor

I think you're on the right track, but look closer at how the force of the left spring is translated through the vertical lever & fulcrum...

If you grab ahold of the block and push it to the right, that compresses the right spring, correct? What does it do to the left spring at the same time? Are the springs working against each other or with each other? How does that change your differential equation?

15. Sep 17, 2015

### mrblanco

If i move the block to the right that would also compress the k2 spring. Aren't the springs working against each other because of the lever? When one pulls in one direction, the other pulls in the opposite direction.

I know I'm missing something here but I can't seem to figure it out

16. Sep 17, 2015

### Staff: Mentor

You're doing fine. Moving the block to the right compresses both springs. So you might as well have one spring on the right only, with what overall spring constant?

17. Sep 17, 2015

### mrblanco

Springs in series so 1/k +1/k2

18. Sep 17, 2015

### Staff: Mentor

Does putting springs in series make them stronger or weaker? Does putting springs in parallel make them stronger or weaker?