# 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.