Find fundamental period of x(t) = cos(Pi * t)

1. Aug 29, 2007

VinnyCee

1. The problem statement, all variables and given/known data

Find fundamental period of $$x(t)\,=\,cos\left(\pi\,t\right)$$

2. Relevant equations

$$x(t)\,=\,A\,sin\left(\omega_0\,t\,+\,\phi\right)$$

Which has a fundamental period $$T\,=\,\frac{2\pi}{\omega_0}$$

3. The attempt at a solution

$$\omega_0\,=\,\pi$$ <---- Right?

$$T\,=\,\frac{2\pi}{\pi}\,=\,2$$

$$T\,=\,2$$

2. Aug 29, 2007

dextercioby

T=2 s. Don't forget the units.

3. Aug 29, 2007

HallsofIvy

Staff Emeritus
"s"? What is "s"? The problem, as stated, does not have units- it is a pure function. Even if you assume "t" is time (I would not, I see no reason to assume this is a physics problem rather than a mathematics problem) why would you assume the units are seconds rather than minutes or hours?

In any case, VinnyCee, your analysis is correct.

4. Aug 29, 2007

VinnyCee

So, are the following correct?

$$x(t)\,=\,cos\left(3\,\pi\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,3\,\pi\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{3\,\pi}\,=\,\frac{2}{3}$$

$$x(t)\,=\,sin\left(4\,\pi\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,4\,\pi\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{4\,\pi}\,=\,\frac{1}{2}$$

$$x(t)\,=\,cos\left(\frac{\pi}{2}\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,\frac{\pi}{2}\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{\frac{\pi}{2}}\,=\,\frac{4\,\pi}{\pi}\,=\,4$$

$$x(t)\,=\,sin\left(\frac{\pi}{3}\,t\right)\,\,\longrightarrow\,\,\omega_0\,=\,\frac{\pi}{3}\,\,\longrightarrow\,\,T\,=\,\frac{2\,\pi}{\frac{\pi}{3}}\,=\,\frac{6\,\pi}{\pi}\,=\,6$$

5. Aug 29, 2007

HallsofIvy

Staff Emeritus
Yes.