What method do you use for questions asking you to prove SHM? I use conservation of energy but am not sure if it's accepted..?!
If you've written out expression for the energy of a system (as a function of position), I think you can find the force by differentiating. So the system is in SHM if the expression for the potential energy is a quadratic (positive quadratic, I.e. Has a minimum) I'm not sure of any of this though.
If you're looking at the same question as me, there is only one string.
If there were two strings, then still use F = ma. It would be T1 - T2 = ma If you sort the lengths properly, the constant bits will cancel out, leaving x double dot = - C x
If you're looking at the same question as me, there is only one string.
If there were two strings, then still use F = ma. It would be T1 - T2 = ma If you sort the lengths properly, the constant bits will cancel out, leaving x double dot = - C x
I meant q7a) on the same section, where there are two strings!
hey, you know in some trig integrals, can you use a substitution in the argument of the trig function like x--> 90-x to change cos to sin and sin to cos...? If you do this do you have to change all the functions?.. but then again wouldn't this make it pointless?
Im just wondering as im useless at substitutions lol
hey, you know in some trig integrals, can you use a substitution in the argument of the trig function like x--> 90-x to change cos to sin and sin to cos...? If you do this do you have to change all the functions?.. but then again wouldn't this make it pointless?
Im just wondering as im useless at substitutions lol
You do need to apply the sub to all the functions, but it's useful. I'm not sure how to explain it exactly, best you work through an example and see for yourself.
hey, you know in some trig integrals, can you use a substitution in the argument of the trig function like x--> 90-x to change cos to sin and sin to cos...? If you do this do you have to change all the functions?.. but then again wouldn't this make it pointless?In isolation, such a transform would indeed be pointless (in general at any rate).
But sometimes you can then combine the integrals to simplify things.
e.g.
I=∫0π/2xsinxcosxdx
The sub you describe lets us deduce that
I=∫0π/2(π/2−x)cosxsinxdx
So far, no progress made. But if we add these:
2I=∫0π/22πcosxsinxdx and we've got rid of that x. From there we can finish quickly:
8I=π∫0π/2sin2x=π.
(Yes, you could do this example using integration by parts, but this isn't always the case).
Does anybody have a copy of the spreadsheet to print out and keep track of which questions you have done that was available on the Prep Thread last year? The link doesn't work, or else it has been taken down.
Does anybody have a copy of the spreadsheet to print out and keep track of which questions you have done that was available on the Prep Thread last year? The link doesn't work, or else it has been taken down.