• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Investigation into factors affecting the time period for oscillations in a mass-spring system.

Extracts from this document...

Introduction

Investigation into factors affecting

the time period for oscillations in

a mass-spring system

When a mass is attached to the end of a spring the downward force the mass applies on the spring will cause the spring to extend. We know from Hooke’s law that the force exerted by the masses attached to the spring will be proportional to the amount the spring extends. F = kx

        When additional downward force is applied to the spring we can cause additional tension in the spring which, when released, causes the system to oscillate about a fixed equilibrium point. This is related to the law of conservation of energy. The stain energy in the spring is released as kinetic energy causing the mass to accelerate upwards. The acceleration due to gravity acting in the opposite direction is used as a restoring force which displaces the mass as far vertically as the initial amplitude applied to the system and the process continues.

A formula that can be used to relate mass applied to a spring system and time period for oscillations of the system is

T = 2π√M/k

This tells us T2 is proportional to the mass

...read more.

Middle

Results

Mass (kg)

Extension (m)

0.100

0.04

0.200

0.07

0.300

0.10

0.400

0.13

0.500

0.17

0.600

0.21

        This gives a value of 28.0 Nm-1

for the spring

 constant of the spring


Time for oscillation - Mass

        The formula T = 2π √M/k can be rearranged to T2 = (4π2/k) M. When compared to y = mx + c we can tell that with T2 on the Y axis and M on the x axis, the gradient will be 4π2 / the spring constant. We can also tell how accurate our results our by checking that c = 0 (i.e. the graph fits comfortably through the origin).

Method

  • Set up apparatus as shown in diagram, making sure the spring hangs totally vertical.
  • Attach the first mass of 100g to the end of the spring and make sure the system is in equilibrium.
  • Pull down on the mass to give the spring potential amplitude of 0.03m and release, simultaneously starting the stopwatch.
  • Record the
...read more.

Conclusion

        The angle at which the amplitude is applied also has a larger effect as the acceleration due to gravity will not act parallel to the motion of the oscillations if the system is not oscillating perfectly vertically. This will cause the system to gradually oscillate further from the vertical disrupting the results even more by the end of all 20 oscillations.

        Another problem with the system not oscillating vertically was that the system began to almost swing rather than oscillate making it very difficult to actually pin-point the exact moment the oscillation was completed.

        This problem would be very difficult to overcome with the experiment been performed manually. If the system was set up in a perfectly vertical plastic tube then the tube was removed just before the amplitude was released we could have more accurate readings as the human eye cannot easily judge how close something is to been vertical. We would then however encounter problems with friction between the plastic tube and the masses. It also proves very difficult to remove the plastic tube without disrupting the amplitude of the oscillation.  

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Waves & Cosmology 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

See related essaysSee related essays

Related AS and A Level Waves & Cosmology essays

  1. Peer reviewed

    Investigate the effect of mass on the extension of a spring.

    3 star(s)

    Fair test: To make sure this experiment is a fair test we must make sure that the spring characteristics are the same after every result. I must make sure I only change the mass on the spring this will change the extension.

  2. Simple Harmonic Motion of a mass-spring system.

    The light spring was hung from the horizontal bar. The horizontal bar was then firmly clamped on a retort stand. 2. The 20g slotted mass was suspended at the other end of the spring. 3. After setting up the above apparatus, the oscillation of the mass was started. B.

  1. Determine the value of 'g', where 'g' is the acceleration due to gravity.

    of the equation as shown below: These are all the calculations required to find the value of gravity and the effective mass of the spring. Measurements The measurements I will need to make in order to determine the values of gravity are the time period, extension and load added on the spring.

  2. The aim of this investigation is to examine the effect on the spring constant ...

    117.50 0.7g 299.67 278.17 599.67 554.67 159.07 137.57 0.8g 346.90 325.40 673.67 628.67 178.33 156.83 0.9g 383.83 362.33 753.33 708.33 197.87 176.37 1.0g 411.33 389.83 828.33 783.33 219.07 197.57 These results tables have been used to plot several graphs which are included.

  1. What factors affect the period of a Baby Bouncer?

    Hence, it is likely that a thicker spring will result in a shorter oscillation period than a thinner spring, provided that other factors are kept constant. * The Amplitude: This is the maximum distance that an object moves from its equilibrium position.

  2. Measuring spring constant using oscilations of a mass.

    To work out k I will have to know the gradient of my straight line. To work out k: M = 4 ?2 / k k = 4 ?2 / M To work out me then I will need to find the intercept of my graph.

  1. An investigation into the time period of a mass-spring oscillating system.

    It requires more energy to move the large mass at the same speed as the small mass. However, if the same amount of energy is used to move the larger mass as the smaller mass, then the larger mass will move slower than the smaller mass.

  2. Hooke's Law / Young's Modulus - trying to find out what factors effect the ...

    the timer, because of this I have decided to time 10 oscillations and then divide the result by 10 this will reduce the experimental error.

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