# 7.8.99 find PS, VS Period, graph

• MHB
• karush
In summary, the amplitude of the given cosine function is 1, the period is 2pi, the phase shift is pi/2 to the left, and there is no vertical shift. The general cosine equation is y = A cos (wx + phi) + y_0, where A is the amplitude, wx is the angular frequency, phi is the phase angle, and y_0 is the vertical displacement.

#### karush

Gold Member
MHB
$\tiny\textbf{7.8.a09 Radford HS}$
Find amplitude, period, PS, VS. then graph.
$y=\cos\left(x+\dfrac{\pi}{2}\right)$For the graphs of $y=A\sin(\omega x - \phi)$ or $y=A\cos(\omega x - \phi),\omega>0$
Amplitude $=|A|$
Period $T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{2}=\pi$
PS $=\dfrac{\phi}{\omega}=\dfrac{\pi}{4}$

well so far
I don't know what the greek letter is for VS or Vertical Shift? which is usually D

$y=\cos\left(x + \dfrac{\pi}{2}\right)$

amplitude = 1

period, $T = 2\pi$

phase shift = $\dfrac{\pi}{2}$ left

no vertical shift

fyi, $\cos\left(x+\dfrac{\pi}{2}\right) = -\sin{x}$

$$\displaystyle y = A ~ sin( \omega x + \phi ) + y_0$$

What was your $$\displaystyle \omega$$ again?

-Dan

topsquark said:
$$\displaystyle y = A ~ sin( \omega x + \phi ) + y_0$$

What was your $$\displaystyle \omega$$ again?

-Dan

 $y=\cos\left(x+\dfrac{\pi}{2}\right)$
well thot it was 2 maybe 4? it was kinda :unsure:

karush said:
 $y=\cos\left(x+\dfrac{\pi}{2}\right)$
well thot it was 2 maybe 4? it was kinda :unsure:

try 1

karush said:
 $y=\cos\left(x+\dfrac{\pi}{2}\right)$
well thot it was 2 maybe 4? it was kinda :unsure:
$$\displaystyle y = cos \left ( x + \dfrac{ \pi }{2} \right )$$

$$\displaystyle y = A ~ cos( \omega x + \phi ) + y_0$$

What is the coefficient of x in your cosine argument??

Geez, dude! You are better than that!

-Dan

topsquark said:
$$\displaystyle y = cos \left ( x + \dfrac{ \pi }{2} \right )$$

$$\displaystyle y = A ~ cos( \omega x + \phi ) + y_0$$

What is the coefficient of x in your cosine argument??

Geez, dude! You are better than that!

-Dan
 $y = \cos \left( 1 \left( x + \dfrac{ \pi }{2} \right )\right )$ are you using $y_0$ as VS

karush said:
 $y = \cos \left( 1 \left( x + \dfrac{ \pi }{2} \right )\right )$ are you using $y_0$ as VS
Yes. There really is no standard way of writing the general cosine equation. It varies from class to class and text to text. (In fact I learned it as sine in College.)

A - wave amplitude
$$\displaystyle \omega$$ - angular frequency
$$\displaystyle \phi$$ - phase angle, or phase shift as you are calling it
$$\displaystyle y_0$$ - vertical displacement, or vertical shift as you are calling it. Some would also call this "h."

-Dan

## 1. What does "7.8.99" refer to in the context of "find PS, VS Period, graph"?

"7.8.99" likely refers to a specific date or time, possibly when an experiment or observation was conducted.

## 2. What is PS and VS period?

PS and VS period refer to the period of primary (P) and secondary (S) waves in seismology. These are types of seismic waves that are used to study the Earth's interior.

## 3. How do you find PS and VS period?

PS and VS period can be found by analyzing the seismogram data from an earthquake. The period is determined by measuring the time between the arrival of the P and S waves at a given location.

## 4. What is the purpose of graphing PS and VS period?

Graphing PS and VS period can help scientists better understand the structure and composition of the Earth's interior. By analyzing the data, they can make inferences about the different layers and materials that make up the planet.

## 5. How is the data for PS and VS period graphed?

The data for PS and VS period is typically graphed using a time-distance graph, where the time it takes for the waves to travel from the earthquake location to a seismograph station is plotted against the distance between the two points. This can help scientists visualize the different wave types and their characteristics.