Natural Frequency: Find Equation of Motion

[mrblanco]

Homework Statement

Find the natural frequency

Homework Equations

On picture

The Attempt at a Solution

Just need help with the equation of motion.

 

[berkeman]

Homework Statement

Find the natural frequency

Homework Equations

On picture

The Attempt at a Solution

Just need help with the equation of motion.

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?

 

[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

 

[berkeman]

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

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

 

[mrblanco]

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

 

[berkeman]

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

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?

 

[mrblanco]

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

 

[mrblanco]

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

 

[berkeman]

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

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?

 

[berkeman]

If I only considered the spring on the right, I get a complex answer...View attachment 88790

That's correct for a single spring and mass (except for the negative sign inside the square root).

http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html

.

 

[mrblanco]

 

[berkeman]

View attachment 88791

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?

 

[mrblanco]

 

[berkeman]

View attachment 88793

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?

 

[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

 

[berkeman]

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

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?

 

[mrblanco]

Springs in series so 1/k +1/k2

 

[berkeman]

Springs in series so 1/k +1/k2

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