Program that will draw a(t) knowing x(t) in SHM

In summary, the conversation discusses an experiment on simple harmonic motion and collecting data of time, displacement, and velocity. The next task is to plot a graph of acceleration, which can be calculated using the first derivative of velocity. However, with 300 results, manual calculation is not feasible. The individual asks for suggestions on programs to automatically plot the graph, as the previously used software has been deleted. Some suggested programs are Labview, Matlab, Origin, and Excel. The conversation also includes calculations for initial displacement and the value of \omega and discusses the possibility of calculating acceleration using a formula.
  • #1
silt
2
0
A few days ago I carried out an experiment about Simple harmonic motion. In the attachment I added the scheme of the laboratory.

I have collected the following data : time(s), displacement(m), velocity(ms-1)

I can obviously plot the graph of x(t). However, the next task is to draw a graph of a(t).
As far as I know, I can calculate the acceleration by using first derivative of velocity. Since I have about 300results I am definitely not going to do it manually :D

Is there any program that I can use to automatically plot the acceleration vs time graph ?
In class we used 'coachlab II', but that little sucker deleted all the graphs when the device was disconnected and right now I have no access to that software.

Cheers
 

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  • #2
You can try Labview, Matlab, Origin, or even Excel. Since you already have the data the work is easy.
 
  • #3
T=0,67s
initial displacement = 0,299m

a=-[tex]\omega[/tex]2*x

[tex]\omega[/tex]=[tex]\frac{2\pi}{T}[/tex]=[tex]\frac{2\pi}{0,67}[/tex]

Since initial displacement is not equal 0, would it be a good idea to calculate it from forumla (initial displacement - displ. at the moment) ?

Are these correct calculations of acceleration ?
 

1. How do I use a program to draw a(t) given x(t) in SHM?

First, input the equation for x(t) into the program. Then, use the derivative function to find the equation for the velocity, v(t), and the second derivative function to find the equation for acceleration, a(t). Finally, plot the acceleration values over time to get the graph of a(t).

2. Can this program work for any equation of x(t) in SHM?

Yes, as long as the equation for x(t) follows the standard form of SHM, which is x(t) = A*cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle.

3. Is it possible to add damping to the SHM equation in this program?

Yes, most programs have the option to add damping to the SHM equation. Damping can be added by multiplying the acceleration equation by a damping coefficient, such as -b/m, where b is the damping constant and m is the mass.

4. How can I change the amplitude or frequency in the SHM equation using this program?

To change the amplitude, simply change the value of A in the equation for x(t). To change the frequency, adjust the value of ω. Keep in mind that the frequency is inversely proportional to the period, so changing ω will also affect the period.

5. Can I use this program to find the displacement, velocity, and acceleration at specific time intervals?

Yes, most programs have the option to input a specific time value and calculate the corresponding displacement, velocity, and acceleration values at that time. This can be helpful in analyzing the motion of an object in SHM at different points in time.

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