• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Spring-damper system with sine input

  • Thread starter gomerpyle
  • Start date
1. Homework Statement

http://s3.amazonaws.com/answer-board-image/ad36bcba0e2d0b49d556f054de19d124.jpg

Variable y(t) is the position of the block of mass m, and u(t) is the position of the plate on the right. The spring is unstretched when y = u. We can think of u(t) as the input and y(t) as the output.

Derive the equation of motion for the block. You should get a second order differential equation
relating the output y(t) and the input u(t).

2. Homework Equations

u(t) = sin3t

Fd = cy'

Fk = ky

F=ma


3. The Attempt at a Solution

The thing that confuses me about this problem is that the spring/damper combo is not fixed to something, but attached to a plate which has a sine input. I know the two forces acting on the mass are the spring and damper, but the sine force acts through those two components so I'm not sure how to represent this in a free body diagram to obtain the necessary equations.

My first thought was this:

my'' = cy'(t)*u(t) + ky(t)*u(t)
y'' = u(t)/m*[cy'(t) + ky(t)]

However, I'm not sure if multiplying the input to both the force of the damper and spring is correct. Could someone help me?
 

vela

Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,403
1,091
The spring exerts a force proportional to how much it's stretched. How do you represent how much it's stretched in terms of u(t) and y(t)?
 
The spring exerts a force proportional to how much it's stretched. How do you represent how much it's stretched in terms of u(t) and y(t)?
Well the spring would be stretched based upon the relative distance between the mass and the plate right? so would it be:

Fk = k*[u(t) - y(t)]

?
 

vela

Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,403
1,091
Yup, and you have a similar situation for the damping term.
 

Related Threads for: Spring-damper system with sine input

Replies
4
Views
2K
  • Posted
Replies
1
Views
1K
  • Posted
Replies
20
Views
2K
Replies
1
Views
1K
Replies
1
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top