# Prempeh College Protest over Defeat; Calls for Review of 2023 NSMQ Finalists

## Prempeh College Protest over Defeat; Calls for Review of 2023 NSMQ Finalists

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**NSMQ Responds to Prempeh College’s Protest – 2023 FinalsÂ **

In a letter Circulating on Social media, Prempeh College, a renowned participant in the National Science and Maths Quiz (NSMQ) competition, has lodged a protest regarding the results of the** 2023 NSMQ Semi-Finals.**

The protest, directed to the Managing Director of Primetime Limited and the Ghana Education Service, outlines their dissatisfaction with the outcome of the 2nd Semi-Final contest held on October 19, 2023, involving **Prempeh College, Pope Johns Senior High, and Opoku Ware School.**

Prempeh College, a historically successful participant in the NSMQ, expressed its concerns about the evolving nature of the competition. They pointed out that missteps and miscalculations by the organizers in the past have negatively impacted their interests.

They highlighted a specific issue related to a riddle presented in the contest, where the answer given by their team, **“principle of superposition**,” was considered equivalent to the response provided by the Physics consultant, “**principle of (linear) superposition.**” They argued that both phrases refer to the same principle and are commonly accepted in higher physics literature.

Prempeh College called for a thorough examination of this matter to ensure fairness and credibility in the NSMQ competition.

They requested that the organizers investigate the issue before announcing the final schools that qualified for the grand finale.

**Simple review of the terms,**

### “principle of superposition” and “principle of (linear) superposition

The terms “**principle of superposition” and “principle of (linear) superposition**” are closely related and often used interchangeably in many contexts, particularly in physics and mathematics.

Both concepts describe the same underlying idea, which is the ability to combine or superpose multiple waveforms, functions, or solutions to linear equations in a manner that preserves linearity.

**In physics**, especially in the study of waves, the** principle of superposition** refers to the ability to** add or superimpose individual waveforms** to find the **net effect**. This principle holds that **when two or more waves meet at a point in space,** their **amplitudes simply add together**.

The term **“principle of (linear) superposition”** may include the word “**linear”** to explicitly emphasize that this principle applies to** linear systems,** where the **superposition property holds**. This is important because in some cases, **non-linear effects can occur**, where the **superposition principle does not apply.**

**Eg Where, Principle of Superposition Does not Apply**

In nonlinear systems, the response to a combination of individual signals at the input will not be the same as the response to the sum of those same signals. The relationship of the impulse response (weighting function) to the frequency response in linear systems is therefore not applicable. The familiar Laplace transform operation (s = Ïƒ + jÏ‰) and the transfer-function concept used extensively in linear systems cannot be applied.

Nonlinear Response is Dependent on Input Signal

The response of nonlinear systems is dependent on the input-signal size and initial conditions as well as the system parameters. A stable response for one input signal may be unstable for another.

In nonlinear systems, phenomena exist that are not present in linear systems (generation of new frequencies, jump resonance, limit cycles, etc). The following are examples of such nonlinear phenomena.Â Source; https://www.sciencedirect.com/topics/physics-and-astronomy/nonlinear-system.

### The principle of superposition

Linear functions are the simplest algebraic functions. They have an important property which is: the sum of two linear functions is as well a linear function. Also, linear equations are the algebraic equations which are the easiest to solve. Using matrices and determinants to solve a system of equations only applies to linear equations.

A system, defined by the function f(x), is linear if the following relationship is true:

f(x1)f(x2)f(x1+x2)=y1=y2=y1+y2

This property is called the Superposition Principle, which can be defined as: if a system (function) responds to the input x1 with the output y1 and it responds to the input x2 with the output y2, it will respond to the sum of the inputs x1 + x2 with the sum of the outputs y1 + y2. With other words, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually.

If the inputs are variable in time, the superposition principle can be written as:

f(x1(t))f(x2(t))f(x1(t)+x2(t))=y1(t)=y2(t)=y1(t)+y2(t)

Based on the definition of the superposition, we can claim that:

any system (function) which respects the principle of superposition is a linear system (function)

the superposition principle applies to all linear systems (functions)

A system (function) is defined as linear if it satisfies the following properties::

f(x1+x2)f(câ‹…x1)=f(x1)+f(x2)=câ‹…f(x1)AdditivityHomogeneity

where c is a scalar (constant).

The Additivity and Homogeneity properties together constitute the principle of superposition.

A more generic definition of the **superposition principle** can be written as: the response y(t) of a linear system due to multiple inputs x1(t), x2(t), â€¦ xn(t), which are acting simultaneously on the system, is equal with the sum of the responses of each individual input, when all the initial conditions of the system are zero. Therefore, if yi(t) is the systemâ€™s response (output) for the input xi(t), the following relationship is valid:

Source; https://x-engineer.org/principle-superposition/

The s**uperposition principle,**[1] also known as **superposition property**, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).

A function F ( x ) F(x) that satisfies the **superposition principle** is called a linear function. **Superposition** can be defined by two simpler properties: additivity

F ( x 1 + x 2 ) = F ( x 1 ) + F ( x 2 )

{\displaystyle F(x_{1}+x_{2})=F(x_{1})+F(x_{2})\,}

source; https://en.wikipedia.org/wiki/Superposition_principle

So, in essence, “principle of superposition” and “principle of (linear) superposition” describe the same basic idea of combining or superimposing linear waveforms or functions. The choice of terminology may depend on the specific context, and whether “linear” is included may be determined by the level of detail or precision needed in a particular discussion as in the Case of the NSMQ.

**You must note that all depends on the specific rules and guidelines set by the NSMQ organizers.**

#### Here is the full Protest Circulating on Social Media

We, the coordinators of the Prempeh College NSMQ Team and Old Boys, acting for and on behalf of Prempeh College, write to register our displeasure at the events leading to the conclusion of the 2nd Semifinal contest of this year’s NSMQ competition held at the Saarah Mensah Auditorium of KNUST Kumasi today, 19th day of October 2023 between 1330hrs and 1700hrs GMT, among Prempeh College, Pope Johns Snr High and Opoku Ware School.

Before going into the gravamen of the matter, we wish to highlight a few things. Prempeh College has since the inception of this competition been a worthy competitor and has been a mainstay of this contest which is evidenced by the number of trophies won by the school since the competition’s inception and has the distinction of being the first school to win the coveted trophy in 1993.

Over the years we have watched the brand grow and expand to attract keen interest from diverse strata

of society. We have always attached seriousness to this endeavour and have been gracious in both victory and defeat. We have however noticed that over time the competition is taking on a computation that does not auger well for the future of the contest.

Over the years we have had to endure a few missteps and miscalculations on the part of the organizers which have been inimical to our interest. We are however constrained at this time to protest and draw your attention to the glaring injustice metcd to us and to seck your urgent intervention to right an obvious injustice and

repair a wrong.

At the said contest during the last round (Round 5), a particular riddle was posed to the teams with

the following clues:

2. Even though there is no theoretical basis for me, I am an experimentally confirmed

principle

PROTEST OF RESULTS OF NSMQ SEMI FINALS AMONG PREMPEH COLLEGE, OPOKU WARE SCHOo

AND POPE OHN’S SHS

We wish to formerly register our protest over the recently announced results of the quiz competition

among the above schools, and call for a detailed examination into a concern raised by our team, in order

to make a new declaration.

The issue bothers on the fact that a riddle answer provided by our contestants as **principle of**

**superposition,** and the one provide by the Physics consultant as the **principle of (linear) superposition**

are the same and are used to refer to same principle.

This fact is common, and is so accepted in higher physics books, as well as most university physics books. We have provided documents to support this as our evidence.

Kindly examine this carefully to make informed decision. So all participants and schools

can fully maintain the level of confidence and credibility of this educative programme.

Based on our concern, we call for the organisers to do immediate investigation before announcing the

final three schools to have qualified for the grand finale.

P.B. Damoah

(Coordinator, PC-NSMa)

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