Finding position of simple pendulum?

[DevonV]

I'm trying to write a program to model a simple pendulum, and I'm having some trouble seeing how I would solve for the position w.r.t. time.

I would ultimately like to be able to specify a length of string, acceleration due to gravity, mass (though I know it has no effect on the period) and angle it's pulled back.

Any help would be great, thanks!

PS: I don't think this qualifies as homework because I'm doing it for fun, but I'm very sorry if I'm wrong!

 

[sleventh]

I'm assuming you are using a pendulum with a dampening force such as air resistance. If not you will be able to exclude the resistive force parameters from this adaptation of Newtons second law, allowing your pendulum to follow free oscillation. the angle in this case is equal to phi and anything following after the symbol $$\cdot$$ is meant to be the time derivative of that variable.
Force=m(L $$\cdot$$ $$\cdot$$$$\phi$$)=restoring force+resistive force
=-mgsin($$\phi$$)-2m$$\sqrt{g/l}$$(L $$\cdot\phi$$) [note: the rsistive force in this case is a obscure example. you will need to create your own depending on what you would like your program to do.

from here you will integrate solving for your angle as a function of time.
$$\phi$$(t)=(A+Bt)e^(-$$\sqrt{g/l}$$t)

[note: the value $$\sqrt{g/l}$$ is considered your dampening parameter which i defined in this case. if you chose to exclude a dampening force or use a different dampening scenario this will not be similar]

to solve for A and B you need to use the first equation and the previous in combination and also set initial parameters. hope this helped!

 

[astrokreng]

I would first like to commend you for taking on this project for fun. Science and programming can be very enjoyable and fulfilling hobbies. Now, let's discuss your question.

To solve for the position of a simple pendulum, you will need to use the equation of motion for a pendulum, which is:

θ(t) = A*cos(√(g/L)*t + φ)

Where:
θ(t) is the angular position of the pendulum at time t
A is the amplitude (maximum displacement)
g is the acceleration due to gravity
L is the length of the pendulum
φ is the phase constant (initial angle)

To solve for the position w.r.t. time, you will need to know the values of A, g, L, and φ. You can specify the length of the string, acceleration due to gravity, and initial angle. The amplitude can be calculated using the initial angle and length of the string. Once you have all the values, you can plug them into the equation and solve for θ(t) at different time intervals.

Additionally, you can also use a numerical integration method, such as the Euler method, to solve for the position at different time intervals. This method involves breaking down the motion into small time intervals and calculating the position at each interval.

I hope this helps you in your programming project. Keep exploring and experimenting, and don't hesitate to reach out for further assistance. Best of luck!