Question

Please write a paragraph: Design an experiment to determine the spring constant of various springs of equal lengths WITHOUT the use of a ruler. Include what material you think you would need and a detailed description of how you would perform the experiment.  

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Answer 1

Here we want to determine the spring constant for various springs. If we can use the ruler than it would have been a simple task, we can simply apply some mass on a vertical spring and directly use the hoke's law for finding the value of spring constant but we are not allowed to use ruler so,

We can make use of the fact that when a system of a block of mass M suspended vertically downward with a spring get displaced from its equilibrium position it starts to oscillate with a time period of

Now to perform this experiment we need spring mass setup, a stopwatch and a counter. Just displace the system from its equilibrium position and start the stopwatch also start the count of total number of oscillation completed in the given time.

Now from this we can calculate the time required for only one oscillation, simply by dividing the two quantities in previous step. We know the value of M already so we can calculate K (spring Constant) using the time period formula. For better accuracy we can repeat it many time (atleast 5 time). and take average of all the iterations.