Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    I am a MSci Physics student and I am stuck on an integral I can't solve, for a problem that initially seems simple but turned out not to be.

    ds(t)/dt = int(t1, t2) [K / s(t)^2]

    K = constant. (t1, t2) are the limits.

    I am not sure how to put formulae into here in a better way.

    Basically I am trying to get a solution s(t) = ......

    However s(t) is part of the problem.

    To put it into physical terms, I am trying to integrate the force felt by a charged particle twice to get the distance it has travelled in time t2-t1.

    Cheers for any help / pointing me in the right direction.
    Offline

    18
    ReputationRep:
    General way to solve these problems:

    \frac{d^2s}{dt^2} = f(s) (in your case, f(s) = K/s^2). Writing v = ds/dt, we observe

    \frac{d^2s}{dt^2} = \frac{dv}{dt} = \frac{ds}{dt}\frac{dv}{ds} (by the chain rule).

    So in fact v \frac{dv}{ds} = f(s). You can solve this to find v as a function of s. So v = g(s) for some function g that you've (just) found. Since this is just \frac{ds}{dt} = g(s), a second integration gives s as a function of t.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 28, 2010
Poll
Do you think parents should charge rent?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.