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Geo-Fry
04-14-2003, 12:53 PM
ok suppose i have a formula with a function in it, and in the parenthesis for it there are two numbers, seperated by a comma, and i dont know what to do
heres the problem:
y(x, t)=y0*exp(-t/n)*cos(2PIft)*sin(PIx/l)
a few things to note-
1.) the part in bold is the part that i dont know what to do with (i dont understand the comma seperating the numbers)
2.) the italics 0 is show that it is variable y zero, not y times zero
3.) exp is a function, where exp(x)=e^x, and e~2.7182818
4.) the following variables are given:
length l=25.5, frequency f=110, magnitude of intial displacement y0=0.5, and characterist decay time n=5
squestions are:
a.) at what location x will the maximum value of y(x, t) occur at t=0? what is that maximum value?
b.) how log does it take for the maximum value of y(x, t) to become y0 to become y0/2?
c.) how long does it take for the value of y(x, t) to drop to an inaudible level (0.01 inches)?
d.) what parameters in the equation would you expect to change if the string was shortened by one half? why?
i dont expect people to answer for me, i dont what them to. but, i have no idea how to even start this. any help is greatly appreciated.

Magos
04-14-2003, 01:23 PM
a.) at what location x will the maximum value of y(x, t) occur at t=0? what is that maximum value?

y(x, t) = y0*exp(-t/n)*cos(2PIft)*sin(PIx/l)

y(x, 0) = y0*exp(0)*cos(0)*sin(PIx/l)
y(x, 0) = y0*sin(PIx/l)

Constants are: y0, PI & l

The function is maximal when sin() is maximal, meaning 1 for v = PI/2.

((PI * x) / l) = (PI / 2)

Shorten by PI:

(x / l) = (1 / 2)

Multiply by l:

x = (l / 2) = (25.5 / 2) = 12.75


The function has its maximum at x = 12.75.

Perspective
04-14-2003, 04:55 PM
Originally posted by Geo-Fry
y(x, t)=y0*exp(-t/n)*cos(2PIft)*sin(PIx/l)
a few things to note-
1.) the part in bold is the part that i dont know what to do with (i dont understand the comma seperating the numbers)



that 'function' in math can be thought of the same way as a 'function' in programming.

ex)

f(x) = 2x + 1
f(3) = 2(3) + 1

for multi-variables...

f(x,y) = 2x + y/x
f(3,4) = 2(3) + 4/3

just think of the x and y (or x and t in your case) as the parameters for your function.

Geo-Fry
04-14-2003, 07:01 PM
ohhh, ok, its all making sense now, thanks a bunch, i appreciate it a lot.