How to Determine u(t) for a Damped System with Step Function Force?

Ploppen
Messages
2
Reaction score
0
Hi everybody!
I have a big question for you, I have been staring me blind on this problem I got.
And wonder if someof you could help mee with it?

the guestion is this:

"Find the time dependent oscillation u(t) for time t>0 for a damped system with one degree of freedome where c=50 kg/s, k=20 000 N/m, m=2 kg and which suddenly affected by a step function force p(t)=po H(t). (that is, the force in zero when t<0 and constant po=1000 N when t>0.) At time t=0 the mass is in the equilibrium position with zero velocity. (easiest to not use Laplace, even though it is one possible way)."

I whould be soo nice if somebody could help me with this task!

thanks!

best regards
//Tobias
 
Physics news on Phys.org
Well, if you know how to do it with Fourier Transform then go for it, but I can tell you how to do it otherwise. Let's work through the algebra first, and put in numbers later because numbers are boring. Fill in between my dots...

I like working with the ODE in the form

\ddot{x} + 2\Beta \dot{x} + \omega_0^2 x = H(t_0)

So for time less than zero it is trivial...

and for greater than zero, you get...

Which when you solve for the ODE will be...

Applying the initial conditions shows...

And plugging them back in gives...

(Possibly expressed fancily by...)
 
I don't have the paper here but I will take a look at it and get back to you in about a week beacuse I have and exam I need to make. And if i don't know how to do it I will ask you for help again if that's okej?!
Thanks for now!
 
Last edited:

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Continuity Equation for a Dimensionless Harmonic Oscillator
Replies
16
Views
2K
Understanding solution to equations of motion of n coupled oscillators
Replies
4
Views
2K
Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
Damped harmonic motion
Replies
3
Views
659
Finding the damping force for a critically damped oscillator
Replies
2
Views
2K
Fourier Transform of product of heaviside step function and another function
Replies
3
Views
5K
Harmonic Oscillator and Volume of Unit Cell in Phase Space
Replies
4
Views
3K
Understanding calculation of 2nd order LTI DE response to step input
Replies
8
Views
1K
Spring with oscillating support (Goldstein problem 11.2)
Replies
7
Views
2K
Damped linear oscillator: Energy losses
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top