# Spring differtiation question

1. Aug 21, 2014

### cracktheegg

1. The problem statement, all variables and given/known data
Differentiation question on physic spring

2. Relevant equations

3. The attempt at a solution

https://www.icloud.com/photostream/#AEGY8gBYGdYO6S;2B1E78BF-9378-47B0-B87C-BD50541B4EE7

Why I can't get the answer given: am I wrong or the answer given wrong

Can anyoneelse work it out and see the answer

Last edited by a moderator: May 6, 2017
2. Aug 21, 2014

### BvU

To put it bluntly: you are wrong.

Don't really appreciate your way of using the template, but never mind. I hope I don't get thrown out of PF for helping anyway. The hint is: integrating $dx\over x^2+7^2$ does not yield a ln. (Check by differentiating !)

3. Aug 21, 2014

### Simon Bridge

For the sake of anyone else checking in: the problem statement is:
You have written $$1200\frac{dv}{dt} = -(v^2+49) \\ \implies t=-\int \frac{1200}{v^2+49}\;dv$$ ... you actually wrote t+c=... but the arbitrary constant gets absorbed into the integral on the RHS.

You show no working for the integration - as BvU suggests, this is where you need to look closer.
You appear to have got: $$\int\frac{dv}{v^2+49}=\ln(-v+7)+\ln(v+7)$$... which would be incorrect.
It is unclear how you did that.

As a matter of routine, you should check your solution to DEs by substituting them back.

4. Aug 21, 2014

### HallsofIvy

Staff Emeritus
$-(v^2- 49)$ factors as $(-v+ 7)(v+ 7)$ but $-(v^2+ 49)$ does not.

5. Aug 21, 2014

### Simon Bridge

Maybe OP read $-(v^2+49)$ as $-v^2+49$ ?

6. Aug 22, 2014

### BvU

Is eggcracker still in the picture ? What of the integral of $1\over x^2+a^2$ ?

7. Aug 22, 2014

### Simon Bridge

'S only been a day ... @eggcracker: any of this helpful so far?
More assistance with feedback.