Everything included in the attached file
Simple Harmonic Oscillation of a Pendulum This experiment will be broken down in three parts. 1. Computational Exploration of Pendulum Motion • Simple Pendulum • Damped Simple Pendulum • Damped Driven Pendulum • Physical Pendulum 2. Experimental • Use Phyphox to take gyroscope data of pendulum motion of the phone. 3. Analysis • Compare the data taken by using Phyphox and compare it to the computational models explored in step 1. Purpose The purpose of this lab is to explore real world analysis to the Simple Harmonic Motion models. Excel (or programing language of your choice) will be used to model and graphically display these relationships and compare the undamped motion to the damped motion. The Euler method will be used in order to make modeling easier for the more compl icated motions. Theory Undamped Simple Pendulum A simple pendulum is described as a mass particle, m, attached to a massless string of length, L. When the mass is displaced an angular displacement from the equilibrium position and released. The gravitatio nal force applies a force causing the object to accelerate, as shown in the picture. This results in an oscillation. ∑ = − sin = = 2 2= 2 2= , where = and α is angular acceleration . Resulting in = 2 2= − sin If we assume theta is small then, 2 2= − This results in a small angle approximation provides an angular position relationship with respect to time, Figure 1 Diagram of the forces acting on a pendulum, taken from Duke Math Site ()= cos ( + ), where = √ and is the phase angle. Damped Simple Pendulum A damped oscillation is when a damping force is present. This damping force is = − = − where b is the dampening constant. If applied to the previous force equation, ∑ = − sin − = = 2 2= 2 2= = 2 2= − sin − This equation becomes more complicated to solve, but if we assume theta is small, then the small approximation yields an angular position function, 2 2= − − ()= −2cos ( + ), where = √ − ( 2)2. Damped Driven Pendulum A driven pendulum is a pendulum that has some damping, but it also has a sinusoidal driving torque. This yields an even more complicated function, = 2 2= sin − + cos () where A is the driving torque divided by the moment of inertia (basically a driven angular acceleration) and is the driving frequency. In order to solve this problem, one must use numerical analysis like the Euler Method. Physical Pendulum A physical pendulum is when you can not use the ball and string method but now you must take into consideration the moment of inertia of the object as it is a defined shape. ∑ = − sin = = 2 2 Resulting in = 2 2= − sin If we assume theta is small then, 2 2= − Figure 2 Physical Pendulum, image taken from HyperPhysics. This results in a small angle approximation provides an angular position relationship with respect to time, ()= cos ( + ), where = √ and is the phase angle. Note this is the equation for a undamped oscillation. If this pendulum is ei ther damped or driven, the necessary terms would be added to the equation. Part 1 – Computational Exploration of Pendulum Motion Exercise #1 Compare the small angle formula to the large angle formula. In order to analyze the large angle formula, you need t o use the Euler Method. The Euler method is a first -order numerical procedure to solve ordinary differential equations. Basically, you take a small step of time and multiply it by the derivate of the value this provides a small change in the value which yo u then add to the prior value to get the new value. For example, if you know the initial position, you can find the next position by adding the initial position to the initial velocity times the change in time. The velocity can be found a similar way. (+ )= ()+ ()∗ (+ )= ()+ ()∗ Using Excel graph both the small angle relationship to the large angle relationship. Are they comparable at small angles? At what angle does the small angle does not match the big angle? Show a graph showing th e difference between the small angle approximation and the Euler method Large Angle approximation. Exercise #2 Now see what happens when you add damping to your pendulum. How does the graph change? What happens if you vary the damp en ing co onstant , b? Is t here still a difference between the small angle approximation and the Euler method large angle approximation at large angles, Is it like Exercise #1? If you change the dampening constant, how does it affect the graph (just do this for one of the models i.e . Small Angle)? Show a graph showing the impact of dampening your pendulum. Exercise #3 Now add the driven torque term , A . Play around and see what happens when you vary A and the driven frequency , . How does it compared to the values learned in Exercises #1 and #2. Note you will need to use the Euler method for this, therefore compare it to the other large angle relationships (in Ex. #1,#2) . Show a graphical relationship of the affect driving a pend ulum compared to just a damped oscillation and a non -damped oscillation. Part 2 – Data Attention ! This part of the lab involves swinging your cell phone. Make sure to perform this experiment over a soft surface and be aware of the cell phones motion. Durha m Technical Community College is not responsible for broken cell phones. Materials Cellphone Phyphox app Either string or a meter stick Tape or a very tight knot . Procedure: 1. ATTENTION!! Make sure you are in a carpeted area and that you are careful with the phone. 2. Weigh your phone. Some phone companies provide this in the specs but don’t forget if you have a case. 3. Either use a rod like a meter stick and attach your cellphone by tape or use string and attach it to your phone, make sure the ph one will not fall off. 4. Open Phyphox, in the menu select Gyroscope , as shown on the left. 5. Press the play button in the gyroscope sensor. Start oscillating the phone, try keeping the angle of oscillation small. You will start seeing data that will look simil ar to the picture on the right. Notice how the Gyroscope z data gives the clearest oscillation graph. This is the graph you will be using. 6. Click on the Gyroscope z data, it will open just the z axis data. Once you have isolated the Gyroscope z data, click on the three vertical dots in the menu bar (next to the trash can). A list will appear. Click on Export Data, in order to send the data in spreadsheet form to your email. Feel free to select what data format you want to use. 7. Now use the data to compare to the models you used in part 1. NOTE: M ake sure you adjust your parameters. The mass is the mass of your cell phone. You may have to shift your data along the time axis as you weren’t able to precisely achieve data the moment it started isolating. Part 3 – Analysis In this part you will be comparing computational analysis to real data. After making adjustments to the data (shifting the axis so your max point is at t=0, this will help with analysis), overlay the theoretical models from Part1 on the data graph from Part2. Play around with the variables and models to see what fits best with your data. Note you, can’t change the mass of your phon e, but you can play around with the idea that it is a physical pendulum instead of a simple pendulum. Is it a damped oscillation? Is it a driven pendulum motion (sometimes holding the string, we tend to influence the motion by adding a driving force.)? Ta sks for the write -up: There will be one writ e up. Include the names of all partners if you had any (one submission per group if you worked in a group.) a. Introduction: Explain what models you are looking at. What variables you kept constant and what variables you didn’t. Then discuss the experiment, the details about the experiment and the parameters: mass and length of string, w hat model you think (hypothesis) will best fit your data. b. Data: Discuss the data that was found, include a graph of the data, note this can be included in the Analysis section. Do you know notice anything interesting in the data? Does it look rather const ant the oscillation or is the amplitude decreasing overtime? Or is the amplitude increasing over time. What did you find when changing models and variables. Answer the questions posed in the lab manual. Include comparison graphs to show how it compares to the data. c. Analysis: Compare the data to the models. Figure out what model and parameters best fit the data and why. (Include a graph of the comparison .) Are there any errors, where could that have come from (no human errors)? d. Conclusion: Overal l understanding of the graphs and the impact the dampening constant and driven force play on the oscillatory motion. Briefly re -iterate what you discovered and why you think that it matches the best with the data. Explain any errors or ways for improvement in conducting the experiment.

The Assignment: Mr. James Quincey, CEO of The Coca-Cola Company (Coke), and his executive team are aware of your skills in strategic analysis. They are asking you to help them assess the situation and
FINAL TAKE-HOME INDIVIUAL ASSIGNMENT Policy Take-home Final Assignment Case Instructions The Assignment Mr. James Quincey, CEO of The Coca-Cola Company (Coke), and his executive team are aware of your skills in strategic analysis. They are asking you to help them assess the situation and to recommend a competitive strategy for the company for the next five years. Please prepare an OUTLINE report for them giving your assessment of the operational situation and your recommendations, considering both strategy formulation and implementation issues. The following two links provide additional financial information about the focal company, Coca-Cola, including latest income statements and balance sheets, both up to the year-end of 2021. https://www.macrotrends.net/stocks/charts/KO/cocacola/financial-statements https://www.macrotrends.net/stocks/charts/KO/cocacola/balance-she Further Instructions & Specifications In addition of these Final Assignment Instructions, please strictly follow the “Structure of Final Assignment Case Analysis Report” enclosed in the end of this document for specific sections and exhibits to include in your case analysis report. Within the case, possible issues, questions, opinions, and even courses of action may have been provided. You may choose to use them or not based on your own judgment; you do not even need to agree with them. Please remember that the creative thinking and unique thoughts shown in your strategic alternatives are key to developing an excellent case analysis report. Keep in mind that your task is to conduct strategic analysis for the company following the provided guidelines, not to resolve a particular issue raised in the case (e.g., a particular debate or an innovation project proposed in the case), even though they might be highly relevant to your analysis. The paper (excluding all exhibits and title pages) must be put on a maximum of three pages in single-space with 12-point Times New Roman font and one-inch (2.54cm) margins on all sides. No text beyond the three pages will be taken into consideration for the grading purpose. The body text of the paper should all be presented in bullet points format only, no paragraphs and lengthy sentences (e.g., over two lines) are accepted (subject to 5% penalty otherwise). The sub-points belonging to a major bullet point, if you use this format, can be put in a smaller 11- point font. Please use the same section headings such as “External Assessment” as given in the “Structure of Final Assignment Case Analysis Report”; do NOT create other headings. Papers that grossly violate guidelines will receive a failing grade or serious penalty at the instructor’s discretion. Please keep an eye on spacing between lines (keeping everything single- spaced), so you can save some space for text. The most important thing is to get it done right (nice and clear and concise), not to elaborate on your points too much. External Research You are not required to conduct any further external research on the company and its industries. Be sure to provide references on a separate page for any search beyond the case and attach this page at the end of the paper. This page may contain only references and can be in addition to the text-pages and exhibits. Continue to see the Structure of Final Assignment Case Analysis Report” Structure of Final Assignment Case Analysis Outline Report Note: These guidelines are intended to help you get the structure right on the case report; meeting them does not guarantee a quality work. Please use the same sections headings (e.g., Key Issues, Current Strategy, etc.) in your paper. Please insert only bullet points (including short sentence) for each section; each point shall be no more than two lines (3-5 words beyond the second line is acceptable in rare cases). If you choose to fill in your points directly on this template, please make sure you remove all instructional words (other than the section titles) for clear presentation. Limit the text to 3 pages (12 font, single-spaced, 1” (2.54cm) margin on all sides), excluding cover pages, tables and exhibits. Key Issues (preferably 3-6 issues each in one bullet point;) Obvious and pressing issues, hidden problems, and long terms challenges facing the company. These issues set a direction in terms of where your strategic alternatives should focus. Please describe them (and number them) in order of importance. External Assessment. Top Three most important opportunities/threats in total, not three each. A table of external analysis (no need to include in the report) will be highly helpful for you to identify good opportunities and threats. Advice: focus on the strategic group of which the focal company is a member, NOT the case company. DO NOT talk about the case company in describing the opportunities/threats. Do NOT give recommendations here as to what firms can do or should do with respect to these opportunities and threats. One sentence describing the strategic group (similar strategy and competitors) Opp/threat #1: One sentence that clearly specifies the opp/threat for the strategic group; 1-2 bullet points following the sentence to provide evidence for the opp/threat Opp/threat #2: ditto Opp/threat #3: ditto Internal Assessment. Top Three most important strengths/weaknesses in total, not three each. Str/weakness #1: One sentence identifying the strength/weakness; 1 subpoint providing evidence; 2-3 separate bullet point arguments explaining the V, R, I evaluation of the strength. If it is a weakness, 1-2 points to discuss whether it can be transformed into a strength in the future. Str/weakness #2: ditto Str/weakness #3: ditto Financial Diagnosis – Exhibit 1 for this section 3-6 bullet points to interpret the ratios in the Exhibit 1. Use various comparisons (e.g., temporal changes) and financial ratios to diagnose the company’s financial situation. Remember to comment on the company’s overall financial health and capacity to carry on future investments that might be part of your strategic alternatives. Current Strategy Note: focus on what the company is currently doing; do NOT discuss what it can or should do in the future Business strategy (one sentence defining the strategy such as differentiation, followed by 1-3 bullet points of explanations) Functional strategy (2-3 separate points for major functional practices such as marketing initiatives); Global strategy and corporate strategy, whenever the case provides information Implementable Strategic Alternatives (a total of TWO alternatives; the most important section!) Note: (1) Business level strategies are expected, while corporate level strategies are accepted. Please do not propose functional level strategies (HR, marketing, etc.) as explained in Chapter 4, which focus on operational changes that aim to improve internal efficiency and effectiveness. Business strategies represent major moves in the way the company competes on the market. They often involve significant investments or divestments that carry long term impact on the company’s competitiveness. These strategies are externally oriented, often answering the question of what to serve, who to serve, where and how to compete. Business level strategic alternatives, often developed based on existing/potential strengths/weaknesses and available environmental opportunities/threats, should deal with key issues (including the pressure for growth). Two alternatives need to be significantly distinctive, yet they all need to generate significant revenue or market growth to the company, which means that simply divesting (stop doing) something may not suffice. Both strategies should go beyond a general goal (e.g., going international or developing a new product) and discuss what the company needs to do exactly (e.g., which country to enter and in what ways? what kind of new product you are talking about exactly?). Remember you do NOT have to use generic strategy terms such as low cost or differentiation to describe your strategy. In fact, you can easily run into cliché ideas if you simply play around these terms rather than explaining specific strategy actions. For example, a strategy of Westjet building leadership in tourism travel segment does not need mentioning any of those generic terms. Both alternatives should be plausible and appealing, supported with solid reasoning and strong arguments. If your two alternative ideas can be easily combined, you probably need to combine them and develop a new alternative. In addition, both strategies should either depart significantly from the firm’s current strategy or add substantive value to the current strategy, showcasing your own contributions. Keep in mind that using status quo or current strategy (that is, continue to do what has been doing) as a strategy alternative demonstrates weak creativity; I need to see your OWN original ideas. Selling off the company is not an option of strategy in the exam. Lastly, a good advice to review your proposed strategy: Do you think the CEO of the firm will find your strategy alternatives useful and implementable? If they do not make sense to the firm (such as ask McDonald to sell luxury hand bags), then you will want to go back and develop some new ones. Alternative #1: One sentence specifying the strategy, followed by 3-5 bullet points of explanations of what it is exactly in terms of specific strategic actions expected from the firm, with respect to the analysis in previous sections Alternative #2: ditto Criteria and Evaluation of Alternatives by Criteria (second most important section) – Exhibit 2-3 for this section One sentence to list 3 criteria (e.g., NPV), and 1-2 sentences to justify your choice of these criteria (that is, why these, not others?) Then, separate points in correspondence to the three criteria, each point using one criterion to compare the two alternatives with clear conclusion (which one is better) and justifications (why). Recommendation and its Implementation 1-2 points to summarize the evaluations and recommend one strategy based on the evaluation 1-2 points to discuss major issues/challenges regarding the implementation of the strategy 1-2 points to discuss the limitations of the recommended strategy with respect to the identified key issues. Offer suggestions on possible solutions if you can. Exhibits (append all exhibits to the end of the paper in the following order) Exhibit 1: Financial Analysis. A table that presents financial ratios of multiple categories, such as profitability, leverage, liquidity, etc., as well as any useful historical comparisons such as sales increase/decrease. No specific ratios are mandatory. All depends on your analysis and needs. Exhibit 2-3: Two Exhibits of NPV corresponding to the two strategic alternatives respectively; put key assumptions, with brief justifications, either at the bottom of the tables or on a separate page. Please refer to the Westover Inn case in your case package for a template of NPV.