Hard proplem for finding sine function

[tinhnho]

hi everyone

here is the question:

Find the sine function which satify these things below:
For t =< 0, f(t) = 0
For 0< t < 1/2, f(t) follows a sine curve with a period of T = 1 sec and peak distance = 1 m
For t >= 1/2, f(t)= 0

anyidea ? thanks everyone

[Guilherme]

I think you could use DFT or FFT.

[tinhnho]

sorry, i dont know what is DFT or FFT.

[Guilherme]

Discrete Fourier Transform

Fast Fourier Transform

[tinhnho]

Originally Posted by Guilherme

Discrete Fourier Transform

Fast Fourier Transform

Here what i get:

sin(pi*t) ; 0< t <.5

is that correct ? it doesn't seem right

[ewmayer]

Originally Posted by tinhnho

hi everyone

here is the question:

Find the sine function which satify these things below:
For t =< 0, f(t) = 0
For 0< t < 1/2, f(t) follows a sine curve with a period of T = 1 sec and peak distance = 1 m
For t >= 1/2, f(t)= 0

anyidea ? thanks everyone

First off, a simple sine function will never be zero outside some finite interval and nonzero inside it, so what you really want is the form of the sine function only in the interval [0, 0.5]. Period of 1 means sin(2*pi*t), so your desired function is a composite of 3 spliced-together pieces:

For t =< 0, f(t) = 0
For 0< t < 1/2, f(t) = sin(2*pi*t)
For t >= 1/2, f(t)= 0

Just plot sin(2*pi*t) between t = 0 and t = 0.5 on your graphing calculator and you'll see it hits zero at either end of the interval.

[tinhnho]

thank you very much