This document contains a multi-part assignment on solving differential equations using Laplace transforms. It includes 5 problems involving concepts like heat transfer, springs, RC circuits, fluid dynamics in interconnected tanks, and the convolution theorem. The problems are to be solved using Laplace transforms and the solutions analyzed graphically or interpreted physically. For most problems, the document prompts setting up the differential equations, taking the Laplace transform to solve, and discussing the implications of the solutions.
Un collarín de 3 kg puede deslizarse sin fricción sobre una varilla vertical y descansa en equilibrio sobre un resorte. Se empuja hacia abajo, comprimiendo el resorte 150 mm y se suelta. Si se sabe que la constante del resorte es k=2,6 kN⁄m, determine:
La atura máxima h que alcanza el collarín sobre su posición de equilibrio.
La rapidez máxima del collarín.
Un collarín de 3 kg puede deslizarse sin fricción sobre una varilla vertical y descansa en equilibrio sobre un resorte. Se empuja hacia abajo, comprimiendo el resorte 150 mm y se suelta. Si se sabe que la constante del resorte es k=2,6 kN⁄m, determine:
La atura máxima h que alcanza el collarín sobre su posición de equilibrio.
La rapidez máxima del collarín.
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Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
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A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
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ECUACIONES DIFERENCIALES
(ASUC01255)
PRODUCTO ACADÉMICO N° 3
Grupo B
2021
JOSE MIGUEL CHOQUECOTA, LOMA (44826640@continental.edu.pe)
CRISTHIANJOSEGUERRA, CERDAN (47681971@continental.edu.pe)
CRISTIANCESAR SAGASTIZABAL, ESCOBAR (10287420@continental.edu.pe)
CARLOS ABEL USCA, QUISPE (73968973@continental.edu.pe)
JONNEL WILMER VARGAS, MONTES (40474605@continental.edu.pe)
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RESOLUCIÓN DE EJERCICIOS
1. La ley de Calentamiento - enfriamiento de Newton establece que la velocidad
con que se calienta (o enfría) un objeto es proporcional a la diferencia entre su
temperatura 𝑇 y la temperatura del medio 𝑇𝑚. Un metal es calentado hasta
alcanzar una temperatura de 140 °𝐶, y a los 2 minutos está a 100 °𝐶. Suponiendo
que la temperatura ambiente está a 27 °𝐶,
a) Formule y resuelva la ecuación diferencial planteada mediante la
Transformada de Laplace, determinando la función que nos proporciona la
temperatura del metal en cada instante 𝑡. Haciendo uso de un graficador
analiza e interpreta el comportamiento de la temperatura en función del
tiempo.
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b) Determine la temperatura del metal a los 6 minutos.
c) Para un tiempo demasiado largo a que valor tiende la temperatura del metal.
(4 puntos)
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2. Considerar una masa de 3 kg y un resorte con una constante de estiramiento k=10
N/m. Al inicio la masa se libera desde el reposo en la posición de equilibrio. Una
fuerza externa 𝑓(𝑡) actúa sobre la masa, siendo la fuerza:
𝑓(𝑡) = 2𝑠𝑒𝑛(3𝑡).
a) Modelar la ecuación del movimiento en ausencia de amortiguamiento (esto
es, plantear el problema de valor inicial).
b) Modelar la ecuación del movimiento en presencia de una fuerza de
amortiguamiento numéricamente igual a la velocidad instantánea
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c) Use la Transformada de Laplace para resolver la ecuación diferencial hallada
en el ítem a) y b).
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d) Luego realice una comparación de las ecuaciones obtenidas como respuesta
graficándolas. (Sugerencia: hacer uso del graficador DESMOS).
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3. En un circuito RLC, adjunto:
Se tiene que 𝐿 = 3𝐻, 𝑅 = 20 Ω, 𝐶 = 0.04 𝐹 y 𝐸(𝑡) = cos(2𝑡). Inicialmente el capacitor
tiene una carga de 5 coulombs y no circula corriente sobre el circuito.
Usando Transformada de Laplace:
a) Determinar 𝑞(𝑡) (donde 𝑞 está en coulombs y 𝑡 en segundos).
b) Grafica el comportamiento de la carga en función de tiempo e interpreta
c) Hallar la cantidad de carga 𝑞 a los 100 segundos.
(4 puntos)
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b. Grafica el comportamiento de la carga en función de tiempo e interpreta
Gráfico de la carga en función del tiempo – Symbolab
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Gráfico de la carga en función del tiempo – Geogebra
Se observaque la carga inicial para t=0 es 5 C , pero a medida que pasa el tiempo va a tender a cero.
c) Hallar la cantidad de carga 𝒒 a los 100 segundos.
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4. Dos tanques, cada uno de 2000 litros de líquido, se encuentran interconectados
por dos tubos. El líquido fluye del tanque A hacia el tanque B a razón de 4 𝑙/𝑚𝑖𝑛.
Los contenidos de cada tanque se mantienen continuamente bien agitados. Una
salmuera con concentraciónde 3 𝑘𝑔/𝑙 de sal fluye hacia el tanque A a razón de
3 𝑙/𝑚𝑖𝑛. Asu vez,ellíquidodel tanque B fluyehacia A a razón de 1 𝑙/𝑚𝑖𝑛, y al exterior
a razón de 3 𝑙/𝑚𝑖𝑛. Si el tanque A contiene inicialmente 50 𝑘𝑔 de sal y el tanque B
contiene 100 𝑘𝑔.
Se pide:
a) Construir un modelo matemático (sistema de ecuaciones diferenciales), para la
cantidad de libras de sal 𝑥(𝑡) y 𝑦(𝑡) presente en el tiempo 𝑡 en los tanques A y B,
respectivamente.
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5. Teorema de convolución
¿Cuál es la importancia del teorema de convolución?
Es muy importante en la solución las ecuaciones diferenciales, ya que evita los
cálculos de ecuaciones complejas como la de fracciones parciales.
¿Cómo se expresa?
¿Es verdad que L-1{F(s)G(s)} = f (t)g(t)? Explique
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A. Determine la transformada inversa de Laplace de las siguientes funciones
usando el teorema de convolución:
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B. Proponer una ecuación diferencial y resolverla aplicando el Teorema de
convolución en el cálculo de la transformada inversa para determinar la
solución de la ecuación diferencial. (Indicar la referencia de texto: título, autor,
año, edición y número de página o indicar la dirección electrónica).
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CAPITULO7 PAGINA 322 EJERCICIO43 , LIBRO DENNISGOZILL ECUACIONESDIFERENCIALESCON
APLICACIONESDEMODELADO.
http://sgpwe.izt.uam.mx/files/users/uami/jdf/EDO/Cap_7_Zill_Laplace.pdf