Finding Frequency of Motion: A Homework Help Request

[rabar789]

Homework Statement

The motion of an object is described by the equation

x = (0.90 m) cos(PI*t/5). I needed to find:

The position of the object at t = 0 and at t = 0.40 s;
I got (0.9) and (0.8718) meters, respectively, which were correct.
The amplitude (0.9 meters) was also correct.

I need to find the frequency (f) of motion.

Homework Equations

x = (0.90 m) cos(PI*t/5)
omega=2(PI)f

The Attempt at a Solution

Finding the frequency is the only thing I can't seem to figure out. I tried fiddling with the "cos(PI*t/5)" equation a few ways, but all of my answers are wrong. I think I may be just dividing by the wrong value or something. Could some one give me a head start? Thanks!

 

[anathema]

Hello, thank you for sharing your progress so far. Finding the frequency of motion is a crucial step in understanding the behavior of the object. Let's start by looking at the equation you provided, x = (0.90 m) cos(PI*t/5). This equation is in the form of a cosine function, where the amplitude is 0.90 m and the angular frequency is PI/5.

To find the frequency, we need to remember that the angular frequency (omega) is equal to 2*PI*f, where f is the frequency. So, we can rearrange the equation to solve for f:

omega = 2*PI*f
f = omega/2*PI

Substituting in the value for omega (PI/5), we get:

f = (PI/5)/2*PI = 1/10 Hz

Therefore, the frequency of motion for this object is 1/10 Hz. I hope this helps and good luck with the rest of your work!

 

[Moetasim]

I am happy to assist you with your homework request. The frequency of motion can be calculated by using the equation omega=2(PI)f, where omega is the angular frequency and f is the frequency. In this case, the angular frequency can be found by looking at the coefficient in front of the t term, which is PI/5. Therefore, the frequency can be calculated as f = omega/(2*PI) = (PI/5)/(2*PI) = 0.1 Hz. This means that the object completes 0.1 full cycles in one second, which is its frequency of motion. I hope this helps you with your homework.