### Equation of Motion for a Vertical Spring-Mass SystemThe objective is to transform the given equation of motion into a system of first-order ordinary differential equations (ODEs) and solve it using MATLAB's `ode45` function. Then, provide a plot of displacement \( y \) versus time \( t \) from 0 to 2 seconds.**Equation of Motion:**\[ m\ddot{y} = -k(y - y_0) - mg \]**Initial Conditions:**- \( y(0) = 1 \, \text{m} \)- \( \dot{y}(0) = 4 \, \text{m/s} \)**Given Parameters:**- Spring constant, \( k = 100 \, \text{N/m} \)- Mass, \( m = 2 \, \text{kg} \)- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)- Initial position, \( y_0 = 1 \, \text{m} \)### Task:- Transform the second-order ODE into a system of first-order ODEs.- Utilize MATLAB's `ode45` for solving the system.- Graph \( y \) against \( t \) for the duration of 0 to 2 seconds.The solution involves converting the second-order ODE into a system by defining:1. \( y_1 = y \)2. \( y_2 = \dot{y} \)This yields:\[ \dot{y}_1 = y_2 \]\[ \dot{y}_2 = \frac{-k(y_1 - y_0) - mg}{m} \]With these equations, code up the system in MATLAB, use the `ode45` solver, and plot \( y_1 \) against \( t \).

The given equation can be written as ODE in state variable form is as given below For the given equation [ 0 , 2 ] is the time period mentioned in the question. [ 1 , 4 ] are the initial conditions given .

Engineering

Computer Science

The equation of motion and initial conditions governing the vertical position of a vertical spring-mass system are given below. Transform this equation into a system of 1st order ODEs and solve the system using MATLAB's ode45 function. Provide a plot of y vs. t from 0 to 2 seconds. mj = −k(y – y) – mg y(0) = 1 m j(0) =4m/s k = 100 N/m m = 2 kg g = 9.81 m/s² Yo = 1m

The equation of motion and initial conditions governing the vertical position of a vertical spring-mass system are given below. Transform this equation into a system of 1st order ODEs and solve the system using MATLAB's ode45 function. Provide a plot of y vs. t from 0 to 2 seconds. mj = −k(y – y) – mg y(0) = 1 m j(0) =4m/s k = 100 N/m m = 2 kg g = 9.81 m/s² Yo = 1m

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Q: (g) the second-largest possible value of and (h) the smallest (that is, most negative) possible…

A: G) Second largest value for l=1 and m1=0 (-1,0,1) second largest is 0 only so COS θ =…

Q: 1. A system defined by the following state-space equations: 日-[ -14 -56 160 1. u = kt2 + b Simulate…

A: We have to write a matlab code of the following state-space equations.

Q: HW10_3 A Using Newton's second law, it can be shown that the period T of a pendulum with length Land…

A: The MATLAB code is as follows

Q: QI/ The ideal gas equation of state is given by: PV=nRT Where: P is the pressure (atm), V is the…

A: In questions with many inbuilt questions, we must answer the first one.

Q: PLEASE EXPLAIN ALL STEPSCreate a truth table of the equation:((((Y AND (NOT Z)) OR ((NOT Y) AND Z))…

A: Note: In the given equation, the number of opening and closing brackets is not equal. The following…

Q: The voltage Ve(t) (in V) and the current i(t) (in Amp) t seconds after closing the switch in the…

A: Here, I have to provide a Matlab code to the above question.

Q: The two blocks of Figure 6.17 are attached to each other by a massless string that is wrapped around…

A: a) The complete free body diagram of the system is presented in the image attached below according…

Q: use matlab code to solve the following question The following equation represents the electric…

A: Here is the matlab code of above problem. see below step for code.

Q: 3. The equilibrium constant for the reaction of chlorine gas with phosphorus trichloride to form…

A: a) Mole balance equation: 0.414 PCl3 + 0.0064 Cl2 ----->0.0086 PCl5 For part b & c mention…

Q: 2. Compute the kinetic energy, in joules, of a 3 g rifle bullet travelling at 300 m/s.

A: So here we have to find kinetic energy so here no programming language is mentioned so we are…

Q: 0.10 units and direction of the resultant force F₁+F₂. units magnitude direction counterclockwise…

Question

### Equation of Motion for a Vertical Spring-Mass System

The objective is to transform the given equation of motion into a system of first-order ordinary differential equations (ODEs) and solve it using MATLAB's `ode45` function. Then, provide a plot of displacement \( y \) versus time \( t \) from 0 to 2 seconds.

**Equation of Motion:**

\[ m\ddot{y} = -k(y - y_0) - mg \]

**Initial Conditions:**

- \( y(0) = 1 \, \text{m} \)
- \( \dot{y}(0) = 4 \, \text{m/s} \)

**Given Parameters:**

- Spring constant, \( k = 100 \, \text{N/m} \)
- Mass, \( m = 2 \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)
- Initial position, \( y_0 = 1 \, \text{m} \)

### Task:

- Transform the second-order ODE into a system of first-order ODEs.
- Utilize MATLAB's `ode45` for solving the system.
- Graph \( y \) against \( t \) for the duration of 0 to 2 seconds.

The solution involves converting the second-order ODE into a system by defining:

1. \( y_1 = y \)
2. \( y_2 = \dot{y} \)

This yields:

\[ \dot{y}_1 = y_2 \]
\[ \dot{y}_2 = \frac{-k(y_1 - y_0) - mg}{m} \]

With these equations, code up the system in MATLAB, use the `ode45` solver, and plot \( y_1 \) against \( t \).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Transforming the equation

VIEW

Creating the function in Matlab to solve

VIEW

Using ode45 function

VIEW

Plot of the y vs t

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Fundamentals of Boolean Algebra and Digital Logics

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

Problem 2 You are studying photoresistors - devices in which the electrical resistance changes in the presence of light. You run an experiment with three resistors - A, B, and C - at various distances from a light source. Write a Matlab program that produces a professional plot of the data. Use the polyfit() func- tion to find the trendline coefficients assuming a power model. Include all three trendlines and equations on the figure. Find appropriate locations for the equations. Distance (d) [m] A (R) [N] | B (R) [N] | C (R) [N] 1 79 150 460 3 400 840 2500 6. 1100 2500 6900 10 2500 4900 15000
MATLAB CODE as if not reiterate..
An aluminum wire having a cross-sectional area equal to 4.60 x 10-6 m? carries a current of 7.50 A. The density of aluminum is 2.70 g/cm³. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire. 1.95E-4 The equation for the drift velocity includes the number of charge carriers per volume, which in this case is equal to the number of atoms per volume. How do you calculate that if you know the density and the atomic weight of aluminum? mm/s
The cross-sectional area: A = (π/4) d^2
The following is used to model a wave that impacts a concrete wall created by the US Navy speed boat.1. Derive the complete piecewise function of F(t) and F()The concrete wall is 2.8 m long with a cross-section area of 0.05 m2. The force at time equal zero is 200 N. It is also known that the mass is modeled as lumped at the end of 1200 kg and Young’s modulus of 3.6 GPa2. Use *Matlab to simulate and plot the total response of the system at zero initial conditions and t0 = 0.5 s
Using python or matlab to compute this.
Write a MATLAB function that calculates the approximate value of six(x) using the Maclaurin series approximation from x-0 to xi+1 six(x) = x -+-+. 3 5 The function should accept 3 parameters: value of x, number of significant figures accuracy i.e. n, and the maximum number of iterations. In the function, use ɛ = (0.5 × 10²-" )% in order to continue until the ɛa falls below this criteria. The function should return 3 values: the approximate value of arctan(x) at the end of the program, final ɛg and the number of iterations it took. Submit short snapshots showing the program running.
How can you tell if a solution of equations has either no solution, one solution, or an infinite number of solutions using Gaussian elimination?
2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye, ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0; 3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions in the variables x_contact, y_contact, and z_contact. Print t_contact = 1.430 X_contact = 0.755 y contact = -0.380 z_contact = (Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial example output above is for ze = 10. 4. calculates the average x- and y-coordinates 1 y = Yi N where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated. Store the result as a list in the variable center = [x_avg, y_avg]…
Please solve using the script attached in the picture.