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

A steel frame is fabricated with the cross section shown

A steel frame is fabricated with the cross section shown. The centered hole allows cables to be run up to equipment above. The frame supports a load P at a distance d from the centroid of the vertical beam. Bending of th ...

The total pressure of a mixture of oxygen and hydrogen is

The total pressure of a mixture of oxygen and hydrogen is 1.65 atm. The mixture is ignited and the water is removed. The remaining gas is pure hydrogen and exerts a pressure of 0.190 atm when measured at the same values ...

An athlete at high performance inhales of air at 10 atm and

An athlete at high performance inhales of air at 1.0 atm and 298 K at a respiration rate of 32 breaths per minute. If the exhaled and inhaled air contain 15.3 and 20.9% by volume of oxygen respectively, how many moles of ...

Airplane fuselages are subject to a variety of complex

Airplane fuselages are subject to a variety of complex loads during flight. Consider a Boeing 777 modeled as a cylinder with 1/4 in wall thickness of 2024 aluminum, 209 ft length and 20.3 ft outer diameter. Assume the cy ...

There are 3 x 103 spheres in a box calculate the number of

There are 3 x 10 3 spheres in a box. Calculate the number of different combinations for the spheres in order to have 1100 spheres in the front third of the box. Assuming that the distribution is normal, calculate the pro ...

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 ...

A rectangular brass column is loaded with a load of p 1500

A rectangular brass column is loaded with a load of P = 1500 lb applied 0.45 in off its centroidal axis. Find the longest permissible length L of the column if the deflection of its free end cannot exceed 0.12 in.

A room has design conditions of78 f db and 50 rh and a rscl

A room has design conditions of78 F DB and 50% RH and a RSCL = 18,000 BTUlhr and RLCL = 8000 BTUlhr. An air conditioning unit supplies 900 CFM of air to the room at 58 F DB and 56 F WB. Will the unit maintain the room de ...

Use eqn 135 to find expressions for the rate of change of

Use eqn 1.35 to find expressions for the rate of change of the expectation values of position and momentum of a harmonic oscillator; solve the pair of differential equations, and show that the expectation values change i ...

1 water in a container is originally at 100 kpa the water

1. Water in a container is originally at 100 kPa. The water is subjected to a pressure of 120 MPa. Determine the percentage decrease in its volume. 2. Determine the height to which water at 68°C will rise in a clean capi ...

  • 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

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

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen