# Mass on a spring - and investigation into resonance

An Experiment to Investigate a Mass on a spring as an Example of Resonance

Method

We set up the apparatus as shown below.  We also included a meter rule to the left of the spring so that we could see the size of the oscillations.

We set the signal generator to produce a sine wave output and set both the frequency and amplitude to a minimum.  We switched on the signal generator and set the amplitude to its middle setting.  We pulled down gently on the load and allowed the spring to oscillate.  We slowly increased the frequency, monitoring the amplitude of the oscillations of the load by reading from the meter rule placed next to the apparatus.  We noted when the amplitude appeared to be at its largest and took this frequency to be the resonant frequency.  We repeated the experiment using different masses and decided to repeat each experiment 3 times for comparison.

Measurements

Before commencing the experiment, we considered what precautions we could take to ensure accuracy.  We placed a meter rule by the apparatus to give us the best possible chance of observing the largest amplitude correctly. We weighed the entire spring system (Weights, hanger and spring as all of these items were involved in the actual oscillation that we were measuring) each time we changed the mass of the system to ensure and accurate reading for mass.  We felt that just adding weights and assuming that the system would increase by exactly 0.1kg would leave too much room for error.  We recorded all of our measurements which are shown below.

We felt that we could improve our accuracy further by performing a couple of trial experiments to see how we could improve upon our initial ideas.  Our trials did not suggest any obvious improvements so we continued with the above method and recorded the following results.

We noted that, in general, that frequency decreased with mass.

Theory

The theory is that resonance occurs at the point where the natural frequency of the spring system is equal to the frequency of the signal generator.

We know that the time period for a mass on a spring is given by

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