Recent content by MaceLee

If you're going to buy a new calculator I would recommend the TI nspire CAS as it does pretty much everything. It's what I use currently to check all my answers.

Okay, I see :) Thanks, will do!

I would assume it means that the action s = \int Ldt is a stationary point (i.e. a min most likely as the action is minimised in real systems). You might want to wait for some confirmation however as I haven't studied Lagrangian mechanics in too much depth.

Ah, indeed. Prior to being told about using limits, I had no idea that you could do so in separation of variables - so I assumed it would work the same way in all cases. Regardless, the overall result an equation which fits the data well; v_0 ends up as you said, around 140. I've just...

Just tried it all in excel. It gives great results :D Thank you very much ehild! Life saver :)

Oh yes, 3 \lambda was written incorrectly, it should have been: 3 \lambda = \frac{103.02}{120000} Sorry about that D: The units are standard, v in ms^-1 and t in seconds. The breaking started at t=10 onwards yes. Your attached graph is a really close fit! I'll try out your new function...

\mu = \frac{301687.25}{120000} 3 \lambda = 103.02 v_0 was set as to satisfy when t = 10, v = 50

Thanks ehild. I tried to use the solution to find predictions for experimental data, but the values are extremely strange. I'm not sure if it's the way I've worked out v_0, but seemingly regardless of the value, the output jumps around really weirdly. The data I'm supposed to be modelling...

Ah silly mistake, I took the tan separately. Thanks again ehild.

Just one last thing! Taking the tangent of both sides gives: kv(t) = kv_0 - tan(\mu t) Taking the k to the other side gives: v(t) = v_0 - \frac{1}{k} tan(\mu t) Where did the denominator come from in your solution? Was it a mistake? Or did I do something wrong again :/ ? Thanks!

Thank you so much, ehild & RoyalCat. I had tried by differentiating it and getting a solution from the second order linear - it works for a few values but then suddenly goes wildly astray. :)

I've been trying for the past day but still can't solve this equation: \dot{v} = -\gamma v^2 - \lambda Where \gamma and \lambda are known constants Could anyone help me please? Thanks!

I've just moved onto the second equation and I'm trying to solve it: \dot{v} = -3\lambda v^2 - \mu Where \lambda and \mu are known constants. I tried to solve it as follows: 3\lambda \int^v_{v_0}v^2 dv = -\mu\int^t_{0}dt Giving: \lambda v^3 - \lambda v_0^3 = -\mu t Resulting...

I see; your solution is indeed much neater. Very much appreciated, I'll remember that in future :) Thanks

I just tried that out, it would seem that the equation isn't plausible. I'll give it another go with linear drag instead. Thanks!