PHYSICS LAB MANUALS

Coupling Constant

Three physical quantities need to be measured in this experiment – time, mass and length.

Make the following table –

Table II : The details of the physical quantities to be measured.
S.No Physical quantity Independent / Dependent Measured with Measuring instrument’s
Minimum Maximum Least count
1 Time dependent stopwatch      
2 Length independent Meter scale      
3 Mass independent Weighting machine      
  1. Measure the spring constant of the coupling spring. (Remember the first semester experiment). Record the data in a table.
  2. Refer to experiment 1. Procedure for measuring the normal mode frequency is described there.

Here the time-period is measured using sensors. Refer to a separate sheet provided to learn how to use the computer interface.

  1. Start the experiment by attaching the coupling spring at the topmost position.
  2. Measure the normal mode frequencies.
  3. Repeat the measurement of normal mode frequencies by attaching the coupling spring at different heights.

How to measure spring constant:

Measure the extension of the spring for different masses attached to it. The spring constant is related to the slope of the line – mg vs extension.

 

length of pendulum = __________m

Mass of pendulum = _________kg

Table III: normal mode frequency measurement.

S.

No.

 Coupling length Fast frequency Beat frequency Coupling strength
    Time period $$T_{1}$$ Frequency $$\omega_{1}$$ Time period $$T_{2}$$ Frequency $$\omega_{2}$$  
  cm s Hz s Hz  
1            
2            
10            

Table IV: beats measurement

S.No.

 Coupling length In phase frequency Out of phase frequency Coupling strength
    Time period $$T_{f}$$ Frequency $$\omega_{f}$$ Time period $$T_{b}$$ Frequency $$\omega_{b}$$  
  cm s Hz s Hz  
1            
2            
10            

Plot the following Graph

Square of out of phase frequency (\(\omega_{2}^{2}\) ) vs square of copling length (\( l^{2}\)) .

  1. Measure the time periods corresponding to the beat phenomenon - Tb and Th. See the details in the theory section.

  2. Calculate \(\omega_{2}\) and \(\omega_{1}\) using the relation given in the theory section. Compare these values with the ones measured in table III