Experiment to calculate spring constant of 2 springs

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Experiment to calculate spring constant of 2 springs

This experiment is concerned with comparing the theoretical period of a trolley tethered between two springs and the actual value calculated by experimentation.

The theoretical period of the trolley can be calculated using the equation:

Where m is the mass of the trolley and  and  are the spring constants of the two springs the trolley is tethered between.

In order to do this, the spring constants for the two masses must be calculated. This is done by attaching one of the springs to a force sensor and measuring the force at distances of regular intervals away from the force sensor. From this, a force against extension graph can now be produced, and the s[ring constant can be calculated using the gradient of this line. This is repeated for each spring in order to calculate the spring constant for both springs. The line given for the graph is of the form, and can be compared to the equation  in order to calculate these spring constants.

In the second part of this experiment, the trolley is tethered between the two springs used above and is displaced from its equilibrium position a certain distance each time. A photo gate is set up to record the time for the cart to pass through its equilibrium position and this can be taken as the period of the cart. The mass of the cart is recorded, and extra mass bars are added to it, in order for the cart to have differing periods depending on what mass is on it. The theoretical period for each of these masses is calculated and compared to the period calculated experimentally.

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Procedure

Apparatus

  • Trolley
  • Two springs
  • Force sensor
  • Dynamics track
  • Photo gate
  • Mass bars
  • Five pattern picket fence
  • Computer with datastudio software
  • Interface

Part 1

  • The interface was connected to the computer, and the data studio document ...

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