Trying to create a simple pendulum angle output on excel

[shocklightnin]

Homework Statement

Trying to create an excel spreadsheet that outputs the angles of a simple pendulum as it slowly comes to a stop.

Homework Equations

so I've used the formula:
θ(t) = θ0cos(squareroot(g/R*t)

where:
θ0= inital angle
g=gravity constant
R= length of string
t=time
i got it off of this website:
http://www.myphysicslab.com/pendulum1.html -where its the answer to the third question.

The Attempt at a Solution

Ive input all of this into a spreadsheet in excel, i was wondering if this is the right equation just to see the output of the angle's descent as the pendulum comes to a stop.

so say you're inital angle is at 90 degrees (you're holding the mass/ball at 90 degrees and then you let it go)
the degree at which it keeps going back and forth from will eventually decrease to zero right? i was just wondering if this was the correct equation for this. if not, could you please help me out?

and if it is:
i have modified the spreadsheet so that the first output of angle in excel will become the next lines' inital angle and repeated it for the following lines. is this a correct way to do this? the output degree does indeed decrease but very slowly. i was just wondering if this is correct.

thank you for your time.

 

[Redbelly98]

I'm a little confused as to what you are doing.

... I've used the formula:
θ(t) = θ0 cos[squareroot(g/R)*t]

(Note, I have corrected the parentheses in the formula)

If you use that equation, the pendulum will keep oscillating and not come to a stop. It's just the cosine function, which is periodic, and its amplitude remains constant for all time. There is no need to take a starting θ value and use it to calculate θ in the following time increment.

To graph θ(t) in Excel, just make a column of time values and a column of θ values using the equation and some suitable values for θo, R, and g. Take note, Excel uses radians when doing trig calculations.

 

[shocklightnin]

Alright, thank you so much for your help.

I just have another question, I've input everything as you said--is it normal for the final out put to have negative values?

thanks again.

 

[Redbelly98]

You're welcome.

It's the cosine function that is being graphed, are you familiar with it? It is perfectly normal for the cosine to have negative values part of the time.

 

[rwisz]

I would first like to commend you for using a reliable source for your equation. The website you mentioned is a reputable source for physics simulations and calculations.

The equation you have used, θ(t) = θ0cos(squareroot(g/R*t), is indeed the correct equation for the angle of a simple pendulum as it slows down. However, it is important to note that this equation assumes that the pendulum is in a vacuum, with no air resistance or friction. In real-life situations, there will be some air resistance and friction, which will affect the pendulum's movement and may cause it to slow down at a different rate.

In terms of your spreadsheet, it is important to make sure that all the units are consistent, as the equation requires the length of the string to be in meters and time to be in seconds. Additionally, it may be helpful to have a column for time intervals, as the angle will change at regular intervals as the pendulum slows down.

Your approach of using the previous line's output as the next line's initial angle is a valid way to simulate the pendulum's motion. However, as mentioned before, in real-life situations, there will be external factors that may affect the pendulum's movement, so the output may not be completely accurate.

Overall, your approach and equation are correct, but it is important to keep in mind the limitations of the equation and the simulation in representing real-life situations. I hope this helps and good luck with your project!