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

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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.

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