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What factors affect the period of a Baby Bouncer?
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To examine what factors determine the period of each oscillation:
- How does the Bouncer’s performance depend on the size of the baby?
- What effect has the sort of support on the bounce?
DIAGRAMATIC REPRESENTATION OF THE SYSTEM:
The oscillation pattern of such a mass-spring system can be characterised as a harmonic oscillator.
CONSIDERATION OF THE THINGS WHICH CAN BE CHANGED IN SUCH AN OSCILLATING SYSTEM:
The things which can be changed in such a system that will impact the period of each oscillation are:
- The mass of the baby (load)
- The material which the spring support is composed of
- The length of the spring support
- The stiffness of the spring support
- The strength of the spring support
- The thickness of the spring support
- The amplitude
[Whether the baby bounces up and down in a vertical manner or whether he or she imparts a rotational motion or forward/backward motion will have some impact on the oscillation period].
The above points are called variables and experiments could be conducted to investigate the effect of changes in each variable (whether absolute, such as changing the material of the spring support, or progressive, such as the addition of progressively large masses to the spring support to determine its elasticity.) In order to perform each series of experiments it would be necessary to keep all of the other components of the oscillating system constant (constants), whilst altering the specific variable to be investigated.
DISCUSSION OF LIKELY IMPACT OF THESE VARIABLES ON THE PERIOD OF OSCILLATION:
Looking at each variable in turn:
- The mass of the baby (load): This is investigated and analysed later on in this report . In summary, it can be seen from the experimental data that the spring used obeyed Hooke’s Law (discussed in more detail later in the report). The spring used was composed of ductile material (a material which can be stretched).
The likely impact of increasing the load on the period of oscillation is that the oscillation period will increase in duration.
- The material which the spring support is composed of: Usually spring supports are made out of metal or rubber. There is an increasing trend, for safety reasons, for the spring support to be made out of rubber. Employing different materials in the construction of the spring support would have a direct effect on the duration period of the oscillation, for example rubber, has a Young Modulus 0.01 GPa, Lead 18 GPa, Aluminium 70 GPa, Brass 90 – 110 GPa, Copper 130 GPa and steel 210 GPa. The Young Modulus is the ratio of stress to strain resulting from tensile forces, provided Hooke’s Law is obeyed.
- Length of the spring support: Because springs are coiled, they can extend significantly even under a relatively small load. The extension is intimately associated with variables such as strength, thickness, material etc. If the wire the spring is made of was not coiled, it would still be possible to stretch it, but this could take a relatively large force.
In practice, most metals are not particularly elastic and usually can only be stretched by circa 0.1% of their original length. Beyond this they become permanently deformed. However, rubber is not as stiff, and strains of several hundred percent are achievable. The period of oscillation of the Baby Bouncer will be affected by the length of the spring support because the longer the support the longer the period of oscillation.
- The stiffness & the strength of the spring: To change the shape of the spring, a pair of forces is required:
When a spring is squashed, (thus shortening it), the forces are compression forces, but when the spring is stretched the forces are tensile forces.
The terms “stiffness” and “strength” sometimes can be confused. However, “stiffness” describes the spring’s inertia to being extended or compressed, whereas “strength” quantifies how much stress (defined as the load acting per unit of cross-sectional area of the wire) is required to reach the point when the material breaks. The value of stress at this point is called the ultimate tensile stress of the material.
It is interesting to note that ductile materials exhibit plastic behaviour beyond the elastic limit and become permanently deformed. The stiffness of the spring support is likely to affect the oscillation period of the system since an increase in stiffness should result in a decrease in period time due to less extension. The higher the strength of the spring, the more likely that the oscillation period will be lengthened.
- Thickness of the spring: With an increase in thickness it follows that the cross sectional area increases. 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. A simple harmonic oscillator moves back and forth between the two positions of maximum displacement, at x = A and x = - A. I believe that the likely impact of an increase in amplitude is an increase in period time as oscillation will increase.
- There are other factors which could affect the oscillation period of a spring in an extremely minor way, such as air resistance, frictional resistance and temperature.
EXPLANATION OF WHY THE PERIOD OF OSCILLATION MATTERS IN THE BABY BOUNCER, PLUS CONSIDERATION OF WHAT THE EFFECT WOULD BE ON THE BABY’S RIDE IF THE FREQUENCY WAS TOO HIGH, OR TOO LOW:
The period of oscillation in a real Baby Bouncer system is of critical importance. This is because the safety aspects of such a system are of paramount importance since a baby is fragile and highly sensitive to stresses and strains. The brain, internal organs, muscular and skeletal systems of an infant at this stage, are in the process of development, hence must be treated carefully.
Additionally, the objective of using a Baby Bouncer from the parents’ perspective is to aid the baby’s preparation for learning to walk and also, used correctly, the baby exercises its legs muscles and can have great fun. Therefore a sensible period of oscillation is desirable for optimum usage and enjoyment.
If the frequency is too high the effect on the baby’s ride could be dangerous, manifesting itself in the baby being shaken around and possible regurgitating it’s food. Also, a high frequency could result in harm to the baby’s muscles and internal organs. The baby could become scared of the Baby Bouncer and anxious about being placed in it on future occasions. Hence, it is vital that the manufacturers of the Baby Bouncer ensure that the spring support exhibits physical characteristics which ensure that this does not happen.
In addition, if the frequency is too high it could create structural faults within the spring, which could create a dangerous situation and may also prevent the bouncer from being safely used again.
By contrast, if the frequency is too low the baby may become bored and find it less fun. Additionally, the spring could eventually become excessively stretched, reducing the eventual elasticity of the spring.
Thus, it can be seen how important it is for companies which manufacture Baby Bouncing systems to carefully conduct experiments in order to determine the optimal system configuration for the product to be sold successfully. It is not just the aesthetic appeal of a bouncing system which will sell it, but more importantly, the safety profile of the system. In the unfortunate event of such a system’s failure it could lead to significant injury to the infant and possible legal implications. (If such an event did occur, the security of fixing the Baby Bouncer to the door frame would have to be examined, in addition to whether the door frame was in good condition, i.e. had physical integrity and was not rotten etc.).
The scientists / engineer’s working for a Baby Bouncer manufacturer would employ a tensile testing machine capable of producing large compressive and tensile forces to investigate the physical characteristics of the spring support.
The oscillation characteristics of any Baby Bouncer system will respond to the range of variables previously listed. In addition, the joint (limb) kinematics and muscle activation patterns produced by infants who have developed differing bouncing skill levels will have impact on the oscillation characteristics of the system. The relationship between several components of bouncing could be determined (in order to investigate the difference between a “skilled” and a “less-skilled” infant in terms of bouncing ability).
The components which could be investigated could be:
- The oscillation pattern of the mass-spring system which can be characterised as a harmonic oscillator ;
- The infant’s contribution to the bouncing behaviour, which can be characterised in part as a forcing function and in part as a harmonic oscillator ;
- The combination of these two components which corresponds to the output (or the bouncing behaviour).
INDIVIDUAL EXPERIMENT – INVESTIGATING THE IMPACT OF ONE OF THE PREVIOUSLY DISCUSSED VARIABLES:
To investigate the impact of mass on the period of oscillation in a Baby Bouncer
I predict that a steady increase in mass will result in a steady increase in the period of oscillation, from my general and scientific knowledge.
It was apparent, from observation of my younger brother when he was a baby, that he was able to bounce very quickly in his Baby Bouncer. The period of oscillation looked to be shorter than the oscillation period when he was six months older, when he had gained considerable weight (mass). Although his leg muscles may have increased in power and size, I believe the predominant reason as to why the period of oscillation on his Baby Bouncer was longer, at an older age, was due to his increase in mass.
Hooke’s Law is a well known law which states that the ‘Extension (x) produced in an object is proportional to the load applied (F), provided that the elastic limit is not exceeded’. This means that an increase in mass will result in an increase in extension length of the spring. Accordingly, the period of oscillation will increase because the spring has to extend further, due to the increased extension. It also means that a decrease in mass results in a decrease in extension, therefore a reduced period of oscillation, due to the spring having to extend less. This can be illustrated below:
Hooke’s Law may be written as F = k x, where k =F / x and is called the spring constant (otherwise known as the spring’s stiffness). This is the force per unit extension, (or the force needed to extend the spring by one metre in length).
Strain is sometimes expressed as a percentage.
The stiffness of the spring material that is undergoing experimental stretching can be calculated by the ratio of stress to strain. This is called the Young Modulus of the material:
YOUNG MODULUS = STRESS ÷ STRAIN
(Young modulus units are usually Pascals (Pa) or Nm -2)
Hence, the Young Modulus is the ratio of stress to strain resulting from tensile forces, provided that Hooke’s Law is obeyed.
The Young Modulus of a particular material making up the spring support of a Baby Bouncer ‘describes’ its degree of stiffness when the material is acting in an elastic way. Hooke’s Law is obeyed until a discontinuity occurs in the physical structure of the spring support and the elastic limit of the material is reached, (thus it approaches breaking point).This did not occur in this experiment.
It is imperative to ensure in a Baby Bouncer that the elastic limit of the spring support is never reached (for safety reasons, primarily).
The elastic limit is the point (just after the limit of proportionality) beyond which the spring support would cease to demonstrate physical elasticity (i.e. in the sense that it does not return to its original shape and size when the distorting force [in this case, the Baby’s weight] is removed).
The point, just after the elastic limit, at which a distorting force causes a major change in the material of the spring is termed the yield point.
In a ductile material, (i.e. a material which can be stretched), the internal structure alters because the intermolecular bonds between the molecular layers break and the layers flow over one another. This change is termed plastic deformation (the material becomes plastic). It continues as the force is increased and the material eventually breaks. [A brittle material, by contrast, will break at its yield point].
This student written piece of work is one of many that can be found in our AS and A Level Waves & Cosmology section.
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