Waste less time on Facebook — follow Brilliant.
×

Help in Solving Physics Differential equation.

Hello everyone!

I'm unable to solve this differential equation while solving a physics question. So please help me in solving this equation:

\[m\frac{dv}{dt}=mg -\lambda\frac{v}{x(x-d)}\] or

\[m\frac{vdv}{dx}=mg-\lambda \frac {v }{x(x-d)}.\]

\(UPDATE\):

\(Here\) \(I\) \(want\) \(to\) \(express\) \(either\)

\(v=f(t)\)

or

\( v=f(x)\).

\(Given\).

where all terms have the usual meaning:

'\(\lambda \)' is constant.

\(v\) is the velocity of the rod (variable)

\(m\) is the mass of the rod (constant)

\(x\) is the distance from a fixed point to the rod (variable)

\(t\) is time (obviously a variable)

and \(d\) is the intial distance (constant)

\(Note\):

This is a part of a question that I'm writing. I'm unable to proceed further because of this difficult differential equation.

Please help! Thanks.

UPDATE

Click here to get full Question Click Here.

Note by Deepanshu Gupta
2 years, 3 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

In the first equation multiply both sides by differential \(dt\).Also write \(v = \frac {dx}{dt}\).

You should get : \(mdv = mgdt - \frac {\lambda dx}{x(x-d)}\)

You also need to know three initial conditions : Initial time which is \(0\),initial position and initial velocity.

Did I make a mistake in doing this? Arif Ahmed · 2 years, 3 months ago

Log in to reply

@Arif Ahmed Yes i did it in same way...!!

But I want to express velocity as either \(v=f(t)\) or \(v=f(x)\) so that further question is completed. Since Both time and distance are different. I mean to say if I want to calculate say velocity at the instant say at t=10 s then how could I know velocity at that instant since position is also unkown at that instant of Time. ?? and Also according to this question \(v = \frac {d(x-d)}{dt}\). which is also same thing as \(v = \frac {dx}{dt}\). Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta I believe the differential equation is not meant to be solved by wolfram alpha itself. Ronak Agarwal · 2 years, 3 months ago

Log in to reply

Hi Deepanshu please try this question. I think you will find this interesting. Satvik Pandey · 2 years, 3 months ago

Log in to reply

@Satvik Pandey @satvik pandey Done..!! Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

Can you please post that whole physics question itself on which you are working. Ronak Agarwal · 2 years, 3 months ago

Log in to reply

@Ronak Agarwal @Ronak Agarwal Ok Done it. You can check it Here. Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Ronak Agarwal @jatin yadav will you help ?? Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta @Calvin Lin sir @Michael Mendrin sir any help?? Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta @Pranav Arora @Finn Hulse any Help?? Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta I don't think I'll be of much help on the problem, but certainly the LaTeX needed editing. Is this the way you would like it to appear? Finn Hulse · 2 years, 3 months ago

Log in to reply

@Finn Hulse Thanks,@Finn But how can I expressed \( v=f(x)\) or \(v=f(t)\).?? which is essential for this question. ( that is my Problem) Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta I'm not sure I understand what you mean. Finn Hulse · 2 years, 3 months ago

Log in to reply

@Finn Hulse Is it possible to express the velocity as an individual function ?? or we require Higher mathamatics?? Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta Are you asking if you can solve for \(v\)? Because if you are, I think it would be very tricky. Finn Hulse · 2 years, 3 months ago

Log in to reply

@Finn Hulse yes.. will you please give a try to it ? I make all possible attempt but not succesfull in it. Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta Sure. Also, I've been to Jaipur! It's super awesome! :D Finn Hulse · 2 years, 3 months ago

Log in to reply

@Finn Hulse wow.. !! A very warm welcome to you for coming in Jaipur..... In our Language we says:

"\(padharo\) \(mhare\) \(desh\)"

Well for what purpose you have been come here... is it Vacation's celebration or something else ? Deepanshu Gupta · 2 years, 3 months ago

Log in to reply

@Deepanshu Gupta I took a trip around Rajasthan and also to Agra (for obvious reasons). I visited Delhi, Jaipur, Udaipur, Bundi, Chittogarth, Ranthambhore, and some other places. :D Finn Hulse · 2 years, 3 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...