Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Mechanical Engineering Expert

Problem Statement
Assume that a simple pendulum is attached to our spring-damper-mass system. A simple schematic of the model is given in Figure .

1713_Pendulum.jpg

The mass can move horizontally where as the pendulum oscillates about a vertical axis attached to this mass.

The problem parameters in their appropriate units are given below in Table.

     Variable              Description            Value
       M               Mass of the body         1.0
       m          Mass of the pendulum       1.0
       k             Spring constant              10.0
      c             Damping Coefficient          0.5
      R         Length of the pendulum        1.0

The equation of motion of the system can be written as:
(M+msin2 θ)x'' cx'+kX-mR(θ')2 sinθ-mgsinθcosθ=0

(M+msin2 θ)R θ''-cx'cos θ-kxcos θ+mR(θ')2sinθcos θ + (m+M)gsin θ=0

with initial condition x(0)=0 x'(0)=0 θ(0)=10°   θ'(0)=0

1. By defining new variables reprepare the equations of motion in the form y '= f (t , y )
2. Solve for the dynamics of the resulting system for 20 seconds of real time using midpoint method. Choose your step size so that the local error is less than 10-4.

3. Plot x vs. t, θ vs. t and θ vs. x on three separate figures.
4. Repeat steps 2 and 3 for θ(0)=90o and  θ(0)=179o while keeping the other initial conditions fixed.

Note: Don’t forget to convert the angles to radians.

Assignment
1. Develop a Matlab function named RK4.m which implements the classical 4-stage Runge-Kutta method (RK-4) for solution of IVPs.
2. Do again steps 2 and 3 by using the RK-4 method as the solution technique. Compare the step sizes used and the CPU times spent by the Mid-point and RK-4 methods.

Mechanical Engineering, Engineering

  • Category:- Mechanical Engineering
  • Reference No.:- M9987

Have any Question? 


Related Questions in Mechanical Engineering

The tires of the 4555-lb sedan are 65 in wide figure p510

The tires of the 4555-lb sedan are 6.5 in. wide (Figure P5.10). Each tire contacts the ground over a distance of 4.25 in. as measured along the vehicle's length. Calculate the compressive stress between each tire and the ...

1 in more than one paragraph but less than a page discuss

1. In more than one paragraph but less than a page, discuss some of the failure modes experienced in the collapse of the World Trade Center and how they might have been prevented. 2. A truss ABC supports a load W at join ...

You need help with these 3 problems to be answered

You need help with these 3 problems to be answered correctly and with an explinations and steps.There are two pictures with three questions, please look and understand them before contacting me as well. 1. An alloy at 10 ...

Many devices have been developed to measure the viscosity

Many devices have been developed to measure the viscosity of fluids. One such device, known as a rotational viscometer, involves a pair of concentric cylinders with radii r i and r o , and total length L. The inner cylin ...

I need research paper of 3 pages about any topics in

I need research paper of 3 pages about any topics in Thermodynamics. 1. Benedictine Orphanage and a new medical building in Tanzania are in need of power supply.  Please design a system which provides power economically ...

1 a differential manometer is used to measure the pressure

1. A differential manometer is used to measure the pressure change caused by a flow constriction in a piping system as shown. Determine the pressure difference between points A and B in psi. Which section has the higher ...

1 what are modes of failure2 what are failure criteria how

1. What are modes of failure? 2. What are failure criteria? How are they related to modes of failure? 3. What is meant by the term factor of safety? How are factors of safety used in design?

The demand for a certain product is a linear function of

The demand for a certain product is a linear function of the price. The sales of the product for three different prices are given in the following table Find the least squares regression line and estimate the demand when ...

Wat is the resilience of the bolts and joint this time

What is the resilience of the bolts and joint this time? What is the stiffness ratio of this eccentric joint? By how much does the tensile load of 7.40 kips increase the tension in the bolts and reduce the clamping force ...

1 the tank is accelerated upward at a uniform rate does the

1. The tank is accelerated upward at a uniform rate. Does the manometer level go up or down? 2. Glass viewing windows are to be installed in an aquarium. Each window is to be 0.6 m in diameter and to be centered 2 m belo ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro