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

Calculate the size h of the two welds required to attach a

calculate the size h of the two welds required to attach a plate to a frame as shown in figure. if the plate supports an inclined force P=50kn. use a factor safety of 3 and yield shear stress of 350 mpa for the weld mate ...

1 a pressure of 10 mpa is applied to 025 m3nbspof a liquid

1. A pressure of 10 MPa is applied to 0.25 m 3  of a liquid, causing a volume reduction of 0.005 m 3 . Determine the bulk modulus of elasticity. 2. The bulk modulus of elasticity for water is 2.205 GPa. Determine the cha ...

The professor took us to trip to a place and told us to

The professor took us to trip to a place and told us to write 3 pages about What do i think about the trip? What was interesting? What is my impression ? https://www.dropbox.com/s/29un7cfm1jify5v/2016-11-26_20-42_0.rar?d ...

1 the v-shaped tank has width w into the paper and is

1. The V-shaped tank has width w into the paper and is filled from the inlet pipe at volume flow Q. Derive expressions for (a) the rate of change dh/dt and (b) the time required for the surface to rise from h 1  to h 2 . ...

1 at what temperature is the kinematic viscosity of

1. At what temperature is the kinematic viscosity of glycerin the same as the kinematic viscosity of helium? 2. According to the Hagen-Poiseuille laminar flow model, the volumetric flow rate is inversely proportional to ...

Assignmentfor this homework you will be creating scripts in

ASSIGNMENT For this homework you will be creating scripts in SciLab. You will turn in electronically, each of the scripts requested below. This is not a group project, so do your own work. Contact me if you have any ques ...

A cable with a length h a cross-sectional area a and

A cable with a length H, a cross-sectional area A, and modulus E is attached to the end of a cantilever beam with length L, second moment of area I, and modulus E (same modulus as the cable). The beam is loaded with a fo ...

Q1 a list three classical methods of optimization in

Q1) a) List three classical methods of optimization in engineering design. b) Describe the type of finite elements used to solve 3 dimensional problems in solid mechanics. Supply examples of the application. c) Describe ...

A steel bar of 100mm length tapers from 12mmtimes10mmfrom

A steel bar of 100mm length tapers from 12mm×10mmfrom one end to 30mm×20mm at the other. If the stress in the bar is not to exceed 100mpa,find the magnitude of the axial force. Also find the change in its length. Take E ...

1 a vertical cylindrical tank having a base diameter of 10

1. A vertical cylindrical tank having a base diameter of 10 m and a height of 5 m is filled to the top with water at 20°C. How much water will overflow if the water is heated to 80°C? 2. A liquid in a cylinder has a volu ...

  • 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