Experiment 8: Nonlinear Oscillator (with damping).

The Damped Nonlinear Oscillator (Pendulum)

 

Introduction:

 

Just like the case of simple harmonic motion, the presence of a damping force, in addition to the restoring force, adds another term c(dθ/dt) to the equation of motion.

Physically, damping leads to dying out of the oscillations with time. Higher the value c, quicker is the reduction of the oscillation amplitude. 

 

Suggested Activities:

 

· For a set of parameters, observe the motion of the pendulum by varying c. You will notice that with increasing c, the oscillations die out in lesser time. In each run, from the graph, find out the t0 at which the amplitude curve crosses zero for the last time. Make a plot of t0 vs. c.

 

· Keeping all other parameters, including c, fixed, vary the mass of the pendulum m, and find out t0 in each case. Make a plot of t0 vs. m.

 

· Similarly, vary the acceleration due to gravity g, and Make a plot of t0 vs. g.

 

· Perform a similar experiment by varying the length of the pendulum L. Plot t0 vs. L.

 

· Do the same thing, by varying θ. What do you observe?

 

· From the above experiments, summarize the effect varying m, g, L and θ on the extent of damping on the motion of the pendulum.

 

 

Questions:

 

Under construction

 

Please feel free to send your feedback, suggestions or queries regarding the experiment to: oscillations.vlab@gmail.com

In your email, please mention the experiment no. and name of the experiment.

 

 

 

 

 

 

 

 

 

 

 
Text Box: Expt. 1. Simple Harmonic Motion Text Box: List of Experiments (click the buttons for each expt.) Text Box: Expt. 3. LC circuit Text Box: Expt. 2. Damped Simple Harmonic Motion Text Box: Expt. 8. Nonlinear Damped Oscillation Text Box: Expt. 4. LCR Circuit Text Box: Expt. 5. Resonance in LCR Circuit Text Box: Expt. 6. Coupled Simple Harmonic Motion Text Box: Expt. 7. Nonlinear Oscillation Text Box: Make sure you have downloaded both the ‘LabVIEW Runtime engine’ and the ‘Vision Runtime Engine’ from the links provided in the main page.

Click here to download the step-by-step instructions video demonstration.
Text Box: go to Main Page

Click here to download the program to run on your computer locally offline (Recommended)
Virtual Laboratory Oscillations

Developed and maintained by: Satyajit Banerjee, Pabitra Mandal and Gorky Shaw

 Procedure for downloading and running programs offline:

· To download the programs, right click on the link above and choose ‘save target as’, or, ‘save link as’ depending on the browser.

· Save the ‘.zip’ file to any directory on your PC.

· Extract the ALL contents of the .zip file to the SAME folder.

· Double click on the file “nonlinear_damped.exe” to start executing the program.

· After this, perform the experiment as demonstrated in the video instructions provided in the link below.