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

Using sketches describe how pwm effectively varies the

Using sketches, describe how PWM effectively varies the average value of the modulated signal. Explain how one could obtain the following by PWM: (a) A zero average (b) A positive average (c) A negative average Indicate ...

Application the dipole antenna a dipole antenna is 1 m long

Application: The dipole antenna. A dipole antenna is 1 m long and is fed with a current of amplitude 2 A. Find the radiated power of the antenna: (a) At 540 kHz (lowest AM band frequency). (b) At 1.6 MHz (highest AM band ...

A creek runs through a certain part of a campus where the

A creek runs through a certain part of a campus where the water is falling about 2.5 mover a distance of just 8 m, and the creek before and after the fall is about 3 m wide. The sustainability club has asked you about th ...

The noise in an electrical circuit can depend on the nature

The noise in an electrical circuit can depend on the nature of the coupling mechanism. In particular, the following types of coupling are available: (a) Conductive coupling (b) Inductive coupling (c) Capacitive coupling ...

In figure 10-c the sleeve-thimble region of three

In Figure 10-C, the sleeve-thimble region of three micrometers graduated in thousandths of an inch are shown. What are the readings for these three micrometers?

A smooth circular cylinder of weight w and radius r rests

A smooth circular cylinder of weight W and radius R rests in a V shape groove whose sides are inclined at angles a and b to the horizontal as shown. Find the reactions RA and RB at the points of conta

Application receive-transmit system two units communicate

Application: Receive-transmit system. Two units communicate with each other at 120 MHz and 10 W; in free space. Unit A uses a half-wavelength dipole antenna placed as shown in Figure 18.46. Unit B uses a 1/100 wavelength ...

Maximum power handling of a waveguide a rectangular

Maximum power handling of a waveguide. A rectangular waveguide has a width to height ratio a/b = 2.0 and the ratio between the operating frequency and the cutoff frequency is f'f c10 = 2.0 at f = 10 GHz. What is the maxi ...

Figure p71 shows a schematic diagram of a stepper motor

Figure P7.1 shows a schematic diagram of a stepper motor. What type of stepper is this? Describe the operation of this motor. In particular, discuss whether four separate phases are needed or whether the phases of the op ...

Application design of sheathing for optical fibers an

Application: Design of sheathing for optical fibers. An optical fiber is made of a glass material with a thin plastic coating as shown in Figure 13.33. Both materials are transparent at the frequencies of interest. Relat ...

  • 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

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate