My Exam Notes
  • Home
  • CURRENT AFFAIRS
  • GENERAL AWARENESS
    • Child Category 1
  • BIHAR PSC
  • Home
  • CURRENT AFFAIRS
  • GENERAL AWARENESS
  • BIHAR GK
  • RAJASTHAN GK
  • MECHANICAL NOTES

Thursday, May 28, 2015

FREE VIBRATIONS

 My Exam Notes     4:28 AM     MECHANICAL VIBRATION     No comments   

MECHANICAL TIPS AND STUDY MATERIAL

Types of Vibrations:

Free vibrations:

This is also called as natural vibration, this is because when a body is vibrating, no extra energy is added to it. Initial energy is provided to start the vibration which slowly and gradually end up with passage of time as energy of the system is liberated or dissipated. As the body starts vibration it tends to move from mean position to extreme position. When it reaches the extreme position, the restoring forces tries to move it to mean position. Such phenomenon is observed in elastic bodies. The forces are proportional to the displacement of the body from the equilibrium position, the acceleration of the body is also proportional to the displacement and is always directed towards the equilibrium position, so that the body moves with SHM.


The number of degrees of freedom of the system determines the different modes of vibration which the body may posses. The motion that all these examples perform is called SIMPLE HARMONIC MOTION (S.H.M.). Consider a simple pendulum which has two degree of freedom. The mass on the spring could be made to swing like a pendulum.


If we will plot the displacement - time graph for above situation, we will get sinusoidal graph. On this contrary I would like to explain that the displacement may be linear or angular. The linear displacement may be distance moved by mass - spring combination and angular displacement may be witnessed by pendulum. 


 Any vibrating body that has a motion that has to be described should must vibrate with S.H.M. and have the same equations for displacement, velocity and acceleration as given below.


Let us consider the Scotch Yoke wheel. The wheel revolves at w radians/sec and the pin forces the yoke to move up and down. The pin slides in the slot and Point P on the yoke oscillates up and down as it is constrained to move only in the vertical direction by the hole through which it slides. The motion of point P is simple harmonic motion. Point P moves up and down so at any moment it has a displacement x, velocity v and an acceleration a.


The pin is located at radius R from the center of the wheel. The vertical displacement of the pin from the horizontal center line at any time is x. This is also the displacement of point P. The yoke reaches a maximum displacement equal to R when the pin is at the top and –R when the pin is at the bottom.


This is the amplitude of the oscillation. If the wheel rotates at w radian/sec then after time t seconds

the angle rotated is q = wt radians. From the right angle triangle we find x = R Sin(wt) and the graph
of x - q 

Velocity is the rate of change of distance with time. The plot is also shown on figure 3a.

v = dx/dt = wR Cos(wt).

The maximum velocity or amplitude is wR and this occurs as the pin passes through the horizontal

position and is plus on the way up and minus on the way down. This makes sense since the
tangential velocity of a point moving in a circle is v = wR and at the horizontal point they are the
same thing.

Acceleration is the rate of change of velocity with time.  a = dv/dt = -w2


R Sin(-w2R)


The amplitude is w2


R and this is positive at the bottom and minus at the top (when the yoke is about

to change direction)

Since R Sin(wR) = x; then substituting x we find a = -w2x


This is the usual definition of S.H.M. The equation tells us that any body that performs sinusoidal 
motion must have an acceleration that is directly proportional to the displacement and is always directed to the point of zero displacement. The constant of proportionality is w2.






  • Share This:  
  •  Facebook
  •  Twitter
  •  Google+
  •  Stumble
  •  Digg
Email ThisBlogThis!Share to TwitterShare to Facebook
Newer Post Older Post Home

0 comments:

Post a Comment

MY TRAVEL VLOG-Being Tourist

Popular Posts

  • Environment Current Affairs 2019 PDF download | Important Questions |
    Watch video on EXAM FOCUS YOUTUBE CHANNEL. Which city of china in only one with all electric taxis? Taiyuan Shenzhen Jingia...
  • TURBOMACHINES
                    TURBOMACHINE DEFINATIONAND  EXPLANATION A turbo-machine is a device in which energy transfer takes place between ro...
  • ENERGY LOSS IN PIPES, Darcy- weicbach formula, Chezy's formula, minor losses in pipe
    MECHANICAL TIPS AND STUDY MATERIAL When ever there is flow of fluid in pipes there will be resistance which add to energy loss. For our stud...
  • #MOST IMPORTANT AUGUST CURRENT AFFAIRS 2018 #PDF link #NOTES #अगस्त करें...
    PDF IS BELOW NOTES - Go Down Notes of August Current Affairs- Navlekha a new platform launched by Google .Google has announced pr...
  • METAL INERT GAS WELDING AND TUNGSTEN INERT GAS WELDING
            TUNGSTEN INERT GAS WELDING (TIG) CHARACTERISTICS IN  BRIEF It is known as GAS TUNGSTEN ARC WELDING (GTAW). Also called Argon arc wel...
  • MAY (1-15th) CURRENT AFFAIRS 2019 | MCQ's | EXPLAINED | FREE PDF |
    PDF WILL BE UPLOADED ON 24/05/2019 The newly elected prime minister of Israel is? Benjamin Netanyahu What is the theme of Internati...
  • #SPACE CURRENT AFFAIRS last 6 months #स्पेस/अंतरिक्ष विज्ञान करेंट अफेयर...
    Indian national committee for space research was established in the year 1962 Indian Space Research Organisation was founded in year 19...
  • BANKING CURRENT AFFAIRS | MD, CEO, CHAIRMAN Of BANKS (UPDATED 2019)| MCQ's | static gk
    This POST is on Banking Awareness 2019 with all important National Banks and its MD/CEO/CHAIRMAN with important points to remember for all...
  • SINGLE PLATE CLUTCH,CONE CLUTCH AND CENTRIFUGAL CLUTCH
                   SINGLE PLATE CLUTCH DESCRIPTION  In the general arrangement it consists of a disc which has frictional material on both its s...
  • CASING OF CENTRIFUGAL PUMP, ITS TYPES AND PRIMING OF TURBINES
    MECHANICAL TIPS AND STUDY MATERIAL CASING OF CENTRIFUGAL PUMP As we know casing surrounds the impeller and guides the water and also raises ...

Categories

AUTOMOBILE BASICS BHIHAR PSC BIHAR PSC biology quiz CURRENT AFFAIRS economics FASTEST MACHINES FLUID MECHANICS GEARS GENERAL AWARENESS HEAT AND MASS TRANSFER I C ENGINE JET ENGINES JOB OPENING IN USA MACHINING PROCESSES MANUFACTURING PROCESS MATERIAL SCIENCE mechanical engineering MECHANICAL JOB VACANCY IN INDIA MECHANICAL VIBRATION MISSILES POLITY QUIZ POWER PLANT ENGINEERING RAJASTHAN GK sports STRENGTH OF MATERIAL THERMODYNAMICS TOP COLLEGES TOP SPEED TURBINES WELDING

Pages

  • QUIZ

Featured post

SCIENCE & TECHNOLOGY CURRENT AFFAIRS 2018 (JANUARY - JUNE)विज्ञान प्रौद्...

CBSE (Central Board of indirect taxes) launched which app to check person collecting GST? GST verify National science day was celebrate...

ad code

Copyright © My Exam Notes | Powered by Blogger
Design by Hardeep Asrani | Blogger Theme by NewBloggerThemes.com | Distributed By blogger Templates