Factors Affecting the Time Period for Oscillations in a Mass-spring System

  • Length: 1331 words (3.8 double-spaced pages)
  • Rating: Excellent
Open Document

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Text Preview

More ↓

Continue reading...

Open Document

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

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

To test this relationship an experiment will have to be performed
where the time period for an oscillation of a spring system is related
to the mass applied to the end of the spring.

Variables that could affect T

Mass applied to spring; Preliminary experiments should be performed to
assess suitable sizes of masses and intervals between different masses
used in the experiment.

Spring constant; The spring constant will be useful to confirm the
relationship. A simple force - extension experiment should be
performed to get an accurate value for k which can be compared to the
value of k from the final experiment.

Amplitude; The amplitude of the oscillations should be kept constant.
Bear in mind the amplitude cannot be larger than the extension caused
by the smallest mass applied to the spring as this would not allow the
system to oscillate properly.

Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »

How to Cite this Page

MLA Citation:
"Factors Affecting the Time Period for Oscillations in a Mass-spring System." 123HelpMe.com. 24 Jun 2018
Title Length Color Rating  
The Development of the Trenches in Spring 1915 Essay - The Development of the Trenches in Spring 1915 The spring of 1915 saw a new frontier develop: the trenches. Trench warfare was one of the main reasons so many men died. It was a ruthless system of warfare, in which lines and lines of men were repeatedly mowed down, one after the other....   [tags: Papers] 785 words
(2.2 pages)
Good Essays [preview]
Middle Eastern Social Movements Essay examples - In recent Middle Eastern social movements Internet-based communication has crucially aided both the potential for mass mobilization and the success of movements. 21st century media technologies (such as Facebook, Twitter, blogging, YouTube, etc.) operate as a semi-public sphere in which people can share dissident attitudes, announce the location of political protests, and coordinate mobilization. Internet-based communication therefore plays a dually important role; it acts as an alternative outlet for individual expression, but it also serves as mobilizing tool to broadcast anti-regime demonstrations, programs, and organizations....   [tags: Mass Mobilization, Success of Movements]
:: 1 Works Cited
1580 words
(4.5 pages)
Strong Essays [preview]
Prepare of National Unity- The Spring and Autumn and The Warring State Period - Prepare of National Unity- The Spring and Autumn and The Warring State Period The Spring and Autumn and The Warring state period, during time 770BC-221BC, also known as the eastern Zhou period. After the emperor Ping of the Zhou dynasty moved to east part, Zhou dynasty began to decline, only keep the name as emperor but do not have the actual control ability. During that time, each country has different social economic conditions under the war. Between nations compete for hegemony the situation appeared....   [tags: Eastern Zhou period, China, culture]
:: 5 Works Cited
2106 words
(6 pages)
Term Papers [preview]
Essay about The School System in the Victorian Period - The school system in the Victorian period School systems throughout the Victorian time period changed, making learning a requirement for everyone, not just the rich families, or the boys. Education was less advanced; they didn’t have a stable school system. The schools didn’t have the technology we have today. The Victorian school systems are different from the current system. The main people to attend school then were the boys. Most poor children did not go to day school, and by 1831, 1,250,000 children went to lessons at the day school....   [tags: current system, poor children, boy]
:: 4 Works Cited
1178 words
(3.4 pages)
Strong Essays [preview]
Investigating How One Factor Affects the Period Time a Mass on the End of a Spring Takes to Complete One Oscillation - Investigating How One Factor Affects the Period Time a Mass on the End of a Spring Takes to Complete One Oscillation Planning Variables ========= The aim of these experiments will be to see how one factor affects the period of time a mass on the end of a spring takes to complete one whole oscillation. One whole oscillation means the mass returning to its original position, be it the equilibrium or not. I will look at the independent variables (variables which are not caused as a result of another variable)....   [tags: Papers] 1175 words
(3.4 pages)
Strong Essays [preview]
Investigating the Oscillations of a Mass on a Spring Essay - Investigating the Oscillations of a Mass on a Spring Aim: In this physics coursework, I'm here to investigate the oscillations of a mass of a spring. In this investigation, the oscillation means the wave moving with periodic regularity. In this investigation, I can use any mass and many springs, so that I can investigate the oscillations. Variables: I believe there are many factors or variables, which can affect the time for 1 oscillation. These can be: · Mass of weight - I believe it will have a very big impact on the time for oscillations....   [tags: Papers] 4704 words
(13.4 pages)
Strong Essays [preview]
The Effect of Mass On a Spring Essay - The Effect of Mass On a Spring Aim: I am doing this experiment to find out what effect mass has on a spring. In order to find out how the spring extends we will need to add various amounts of weights to the spring. Apparatus: Ÿ Stand Ÿ Clamp Ÿ Spring Ÿ Weights (Newton's) Ÿ Metre Ruler Ÿ Goggles Diagram: Method: Once I have all my apparatus set up like above, I will measure the spring on its own to find its original length. Once I have written down the measurement in mm's, I will add 1 Newton onto the bottom of the spring....   [tags: Papers] 380 words
(1.1 pages)
Strong Essays [preview]
Essay on Prague Spring - The Prague Spring The Prague Spring is referred to when the Warsaw Pact allies invaded Czechoslovakia in 1968. Below are the details surrounding the incident. In 1948, communism was the only political party in Czechoslovakia. The communist take-over was a very popular movement. The first reason why it was a popular movement is because Joseph Stalin signed an agreement with Winston Churchill and Franklin Roosevelt that the Red Army, which would then lead to pro-communism, would liberate Czechoslovakia....   [tags: History Prague Spring Invasion] 1440 words
(4.1 pages)
Strong Essays [preview]
The Rites of Spring by Modris Eksteins Essay - Modris Eksteins presented a tour-de-force interpretation of the political, social and cultural climate of the early twentieth century. His sources were not merely the more traditional sources of the historian: political, military and economic accounts; rather, he drew from the rich, heady brew of art, music, dance, literature and philosophy as well. Eksteins examined ways in which life influenced, imitated, and even became art. Eksteins argues that life and art, as well as death, became so intermeshed as to be indistinguishable from one another....   [tags: Eksteins Rites Spring] 1030 words
(2.9 pages)
Good Essays [preview]
Essay about The Conflicted Japan of Yukio Mishima’s Spring Snow - The Conflicted Japan of Yukio Mishima’s Spring Snow Yukio Mishima was a revolutionary author. His dramatic public suicide is the perfect capstone to a life full of turmoil and unrest. Mishima himself was as conflicted as his many stories and plays, which tend to play out the problem of which direction is Japan heading, and should the nation be developing that way. Mishima romanticized the samurai and nurtured a lifelong affair with traditional Japanese theater. At the same time, he admired the West and studied Western art and literature avidly....   [tags: Spring Snow] 1627 words
(4.6 pages)
Strong Essays [preview]

Related Searches

Elastic limit of spring; If the spring has been extended past its
elastic limit it will have become permanently deformed and will no
longer obey Hooke's law causing inaccuracies in the readings.

Preliminary Experiment

From preliminary experimentation I found that;

· 0.03m is a suitable amplitude to give appropriate sized oscillations
with minimal disruption at lower masses.

· Due to a ±0.01s error in the stopwatch it is sensible to only take
readings of 1 by taking the time for 20 oscillations and using that data to find the
time for a single oscillation.

· Intervals of 0.1kg between masses of 0.1kg and 0.7kg give a wide
range of readings without putting excessive strain on the spring.

No particular concern to safety is required under these conditions. If
larger masses were to be used safety goggles would need to be worn in
case of the spring snapping.


0.100kg masses - The 7 100g masses I am planning to use in my
experiment actually have an average mass of 0.098kg meaning there is a
percentage error of around 2% in the masses I am using in my
experiment. Although this is a larger error than would be preferable,
if the same masses are used in both the force - extension experiment
and the mass - oscillation experiment the values for the spring
constant should still be comparable.

Stopwatch ±0.01s - From preliminary experimentation I know that the
smallest time I will probably have to measure will be around 6-7
seconds. This means than the largest percentage error I should
encounter in the timing will be around 0.17% which will be negligible
in this experiment.

1m Ruler ±0.001m - The smallest measurement I will have to take will
be the 0.03m amplitude of the oscillations. The percentage error in
this measurement will be about 3.3% which is quite large but if the
amplitude was changed so as to give a percentage error of 1% or below
we would have to use an amplitude of at least 0.10m which would not be
possible at masses under around 0.300kg.

Spring - If the spring has been permanently deformed prior to the
experiment it will no longer obey Hooke's law (F = kx) so we will not
be able to use the calculated value for the spring constant from the

force - extension experiment.

The main factor that will effect the experiment will be human error.
It is very difficult to define exactly when an oscillation starts and
ends and almost impossible to actually get the system to oscillate
perfectly vertically. Also factors such as reaction times will have a
significant effect on the results from the experiment.

Force - Extension

To determine the spring constant of the spring been used, a force /
extension graph can be plotted. Using Hooke's law we can see that if
force is plotted on the Y axis and extension is plotted on the X axis
the gradient will be the spring constant. In this case Mass is been
plotted on the Y axis so the spring constant will be the gradient
multiplied by g (9.81ms-2).


· Set up the spring so as it hangs securely from a point high above
the work area.

· Attach a mass of 100g to the end of the spring and measure the
amount which the spring is extended by.

· Repeat the process at 100g intervals up to 600g recording the
extension at each mass.


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 4Ï€2 / 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 amount of time the system took to oscillate about its
equilibrium point 20 times and stop timing.

· Repeat the process at intervals of 100g up to 700g performing the
test 3 times at each mass for accuracy.



Mass (kg)

Time for 20 oscillations (s)

Average time for 1 oscillation (s)

Average time for 1 oscillation squared (s2)











































These results give a value of 25.6 Nm-1

for the spring constant of the spring.

Analysis / Evaluation

The spring constant of the spring was calculated as 28.0 Nm-1 from my
mass - extension experiment. This can be taken as a reasonably
reliable calculation as the experiment did not have much potential for
human error, there were less variables to be considered and my graph
confirms the relationship F = kx (Hooke's law) as it is a straight
line through the origin.

There are some slightly anomalous points on the mass - extension graph
probably due to the 2% error in the masses used or due to the spring
becoming slightly deformed during the experiment.

As predicted from the relationship T = 2π√M/k, as the mass applied to
the system increases, the time for an oscillation increases
exponentially. The relationship can be confirmed as the graph of T2
against M is a straight line through the origin.

The spring constant calculated from this graph was 25.6 Nm-1 which is
comparable to the 28.0 Nm-1 from the first experiment. Taking 28.0 Nm-1
as the 'actual value' (as it was calculated from a more reliable
experiment with a simpler relationship) we have a percentage error of
8.6% between the two values with no particularly apparent anomalous

The error in the apparatus only came to around 2.021% (2% of that been
the inaccuracies in the masses used) so most of the error came from
the practical difficulties in actually performing the experiment.

The experiment was probably not entirely suitable the main problem
been trying to get the system to oscillate as vertically as possible.
If the system oscillates at just 10 degrees off the vertical then only
98% of the amplitude actually acts on the vertical component of the

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

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.

Return to 123HelpMe.com