newbie: explicit function works, "function object" doesn't

*To*: mathgroup at smc.vnet.net*Subject*: [mg96207] newbie: explicit function works, "function object" doesn't*From*: Tom Roche <tlroche at gmail.com>*Date*: Mon, 9 Feb 2009 05:35:29 -0500 (EST)

summary: I've got a function that I can Manipulate, but I can't Manipulate the things to which the function is assigned. I'm assuming this is due to a syntax error. details: As advertised by the Subject:, I'm new to Mathematica (specifically M7 running on a linux cluster) so please excuse any lapses in terminology. I'd also appreciate pointers to specific docs rather than just an RTFM. Also feel free to refer to my notebook @ http://www.unc.edu/~tr/classes/GEOL861/hw1Notebook.nb I'm trying initially to model a linearized pendulum theta''[t] == -omega^2 theta[t] (where omega=g/l) with the simple initial conditions theta'[0]==v0 theta[0]==theta0 Using soln = DSolve[{linearPendulum, theta'[0] == v0, theta[0] == theta0}, theta[t], t] I get the solution theta[t] -> (omega*theta0*Cos(omega*t) + (v0*Sin(omega*t)))/omega However, when I try to Manipulate[Plot[soln...]], I get ... nothing. Not an error, and I do get the appropriate UI, but I don't get a plot. >From what I've read, it seems Manipulate wants an expression like the RHS of 'soln', which I'll refer to here as a "function." (Please correct my usage as needed.) I got a "function object" with ReplaceAll happysoln[t_] = theta[t] /. soln[[1]] similar to a working example I've seen. But Manipulate[Plot[happysoln...]] also fails silently, like the previous. However, when I manipulate the "function" directly Manipulate[Plot[(omega theta0 Cos[omega t] + v0 Sin[omega t])/omega, {t, -2 Pi, 2 Pi}], {{omega, 1}, 0, 5}, {{theta0, 1}, 0, 5}, {{v0, 1}, 0, 5}] it works as designed: I get the UI with the plot, which I can twiddle with the sliders. Why can I Manipulate the function, but not the containers of the function (i.e. soln, happysoln)? More importantly, with what syntax can I Manipulate those containers? TIA, Tom Roche <Tom_Roche at pobox.com>

**Follow-Ups**:**Re: newbie: explicit function works, "function object"***From:*Murray Eisenberg <murray@math.umass.edu>