• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5

# Mass on a spring - and investigation into resonance

Extracts from this document...

Introduction

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.

Middle

1.61

0.499

2.00

1.2

1.2

1.2

1.20

1.44

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

T= (2π)(√(m/k)) but we also know that f = 1/T so

f = 1/T = 1/ ((2π) (√(m/k))

= (1/(2π)) (1/(√(m/k))

= (1/(2π)) (√(k/m)

So

f² = ((1/(2π)) (√(k/m))²

= (1/(2π)² (√(k/m))²

= (1/4π²)(k/m)

= (k/4π²)(1/m)

I have included columns in the results table for 1/m and f² as f²= (k/4π²)(1/m) which is in the form y=mx+c.  This means that a graph of f² plotted against 1/m should give us a straight line with a gradient of k/4 π², which means we will be able to find the spring constant k (See graph 1).

From my graph the gradient = 0.568 so

0.568 = k/4 π² which means

k = 0.568 x (4 π²) = 22.42 N/m

In order to verify this we performed a further experiment.  Using the equipment set up in its original format, we taped the string to the meter rule in order to keep the spring stationery.  We then measured the extensions of the spring, at rest, firstly without weights and then with the individual weights previously used.  We recorded the following results.

 Mass (Kg) Spring extension (m) Spring Constant K(kg/m) Spring Constant k (N/m) 0.107 0.041 2.61 25.6 0.205 0.081 2.53 24.82 0.303 0.120 2.53 24.82 0.400 0.161 2.48 24.33 0.499 0.202 2.47 24.23

Conclusion

In order to improve the experiment I would attempt to measure the natural resonance of the spring using a stop watch and the meter rule for comparison purposes.  We could also add a Perspex tube in which to place the spring and load to prevent the spring from swinging.  However, we would need to ensure that the spring did not hit the side as this may affect results.

Ideas for further research

We could research whether or not a spring moving in any direction other that up and down, ie swinging during the experiment would materially change the results.  We could also investigate what would happen if we damped the oscillation by repeating the experiment with the load suspended in water.  Initial thoughts would be that the velocity of the oscillations may be reduced but we would be more concerned with whether or not the amplitude of the wave had changed and thus the frequency of the natural resonance,

This student written piece of work is one of many that can be found in our AS and A Level Mechanics & Radioactivity section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related AS and A Level Mechanics & Radioactivity essays

1. ## Catapult Investigation

3 star(s)

As you can see the line is not straight. This is how we known straight away that it does not increase proportionally. The graph shows a smooth increasing in height and steepness curve. Points with Newton force of 4, 6 and 10 do not seem to fit the line of best fit.

2. ## OCR B Advancing Physics Physics Practical Investigation Coursework Investigating Simple Harmonic Oscillations

Increasing k would mean a larger amount of energy could be stored in the spring - increasing displacement and frequency and decreasing the period, in accordance with the equation: T= 2? V(m/k) Changing the diameter of the cylinder containing a constant volume of water may also have an effect upon

1. ## Role of the RAF in second world war

According to Douglas Bader, a Group Captain in the Royal Air Force, the Spitfire and the Hurricane both had smaller turning radiuses than the Luftwaffe fighters did9. Therefore, in order to keep out of an enemy gun sight, RAF pilots simply had to turn hard.

2. ## Find out the difference in flight time, of a weighted paper helicopter, on comparison ...

A way of increasing an object's rotational momentum is to put most of its mass as far from the centre of rotation as possible as this will maximise its speed and therefore give it more momentum. If a spinning object has more momentum when its mass is far from the

1. ## Helicopter Investigation

I am to cut along and fold along the lines as described: Where the dotted lines are shown this is where we are to fold along, and where the straight solid lines have been drawn in, we are to cut along them.

2. ## Use of technology in a hospital radiology department. The department of imaging is one ...

injected, ingested, or inhaled, the radioactive isotope decays resulting in the emission of gamma rays. This gamma ray gives us a picture of what's happening inside the patient's body. However the components making up the gamma camera are the collimator, detector crystal, photomultiplier tube, position logic circuits and the data analysis computer.

1. ## Multi-bladed Pumps. Does the number of propellor blades affect the efficiency of a ...

Ensure all water-containing equipment is as waterproof as possible, and have towels to hand to soak up spills. Do not leave the set-up unattended without unplugging the mains supply. Preliminary findings In the research and rationale section, I identified variables I wanted to investigate.

2. ## Given a Batch of Factory Springs, Estimate the Average Spring Constant and Uncertainty of ...

If this is the case, I will hang a small mass (20 g - 50 g) from the spring initially and consider that to be the spring's starting position. Making a small pointer out of a bent paper clip and fixing it to the end of the spring acts well

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to