• 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...


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.



Mass (kg)

Extension (m)













        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).


  • 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.


        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. Investigating the relationship between the mass and time period in a spring-mass system

    remembering to stop the clock when the bottom of the height-hanger will past the pointer. 15. Record obtained value in the table. Record also the number of oscillations for which the time was measured. Divide the time by the number of oscillations.

  2. Measuring spring constant using oscilations of a mass.

    The accurate value for me is 9.0 g. Re -arranging the formula of the intercept will tell me how to work out me: C = 4 ?2 x me / k me = C x k / 4 ?2 Preliminary Results Spring Constant Preliminary Results No.

  1. Investigating factors which affect the period of an oscillating spring

    the time change between masses on average was 1.1 seconds therefore I can predict that if I had used a larger range of masses then I would find that the change between readings would be zero because the springs elastic limit will be reached and the spring would not return to its normal size.

  2. 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.

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

    I have therefor completed tables below of the actual extension of the spring in each case. These extension values have been found by subtracting the original length of the spring (found before conducting each experiment) from the total length shown in the above tables.

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

    28.7769 - 27.4 = 1.3769 = 0.047 x 100 = 4.7 28.7769 The difference between the two sets of results is 4.7 % From my results from both experiments I can see that as load increases so does extension of a spring.

  1. Investigating the Vertical Oscillations of a Loaded Spring.

    for 10 oscillations and then divide this by 10 to get time period per oscillation. This should hopefully improve accuracy. * 5 different masses recorded, repeating each mass three times to get an average, again to improve accuracy. Apparatus: * Retort Stand and accompanying clamps. * The spring under investigation.

  2. An Investigation into the Factors, which affect the Voltage Output of a Solar Cell

    I then began to cover up the solar cell, which was facing the ray box. I did this 1cm at a time until the whole solar cell had been covered, careful as I held the card not to obstruct the light shinning on the rest of the solar cell that was revealed.

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