How Is Work Calculated in a Forced Oscillation with Resistance During Resonance?

  • Thread starter Thread starter bour1992
  • Start date Start date
  • Tags Tags
    Oscillation Work
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
4 replies · 2K views
bour1992
Messages
11
Reaction score
0

Homework Statement


How can I calculate the work which is produced by the resistance force in a forced oscillation in one period?
The only forces on the oscillatory body are the resistance force and the external force.
The oscillatory body is in resonance.

Homework Equations


resistance force: [tex]F_{res}=-bv[/tex] (b is the damping constant)
external force:[tex]F_{ext}= F_{max} \cbullet \cos\omega t[/tex]
[tex]x=Asin\omega t[/tex]
[tex]u=u_{max}cos\omega t[/tex]Thanks in advance
 
Physics news on Phys.org

Discussion

How can you calculate work in general?

ehild
 
the work in a constant force is: W=F*d.
Moreover the work can be calculated from the area from graph F-d.

I can't find the work with either ways.
 
A definition of work can be found in this http://en.wikipedia.org/wiki/Work_(physics)" .
 
Last edited by a moderator:
bour1992 said:
the work in a constant force is: W=F*d.
Moreover the work can be calculated from the area from graph F-d.

I can't find the work with either ways.

The work is not constant here, and the area can be calculated as integral of force with respect to the displacement.

There is an other way to get work, by integrating power with respect to time for a given time period. And power (P) is the scalar product of force (F) and velocity (v). In case of one-dimensional motion,

[tex]P=Fv[/tex], and work done in one period is

[tex] W=\int_0^T{F(t)v(t)dt}[/tex]

You know that [tex]F =-bv[/tex], and [tex]v(t)=v_{max}cos(\omega t)[/tex]. Write the product of them and integrate.

ehild