Physics igcse 2012 exam revision notes by samuel lees and adrian guillot 1. We begin by defining the displacement to be the arc length. The pendulum 1 introduction instructional physics lab. Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression for its period. For small displacements, a pendulum is a simple harmonic oscillator. This resource manual outlines the basic expectations for each lab, the use of some but not all of the important equipment and software, and other miscellaneous information that may prove useful. A simple pendulum consists of a small bob suspended by a light massless string of length l. M it a special type of periodic motion in which the acceleration of the body along the path of the body is directed towards a fixed point in the line of motion and is proportional to the displacement of the body from the fixed point.
Lecture 2 vertical oscillations of mass on spring pendulum damped and driven oscillations more realistic outline. A road drill vibrates up and down with shm at a frequency of 20hz. The linear displacement from equilibrium is, the length of the arc. Heavy damping occurs when the resistive forces exceed those of critical damping. Dec 25, 2015 this animation shows the forces applying to a damped pendulum. Damped pendulum motion has been investigated both theoretically and experimentally for decades. While they rightly pointed out that several parameters of the experiment such as velocity and strength of the magnet and the number of.
The simple pendulum 1032014 page 4 you can compute g from the period of the pendulum and the length of the string. In this lab, youll explore the oscillations of a massspring system, with and without damping. Rev 01 january 31, 2007 the pendulum laboratory 1, physics 15c due friday, february 16, in front of sci cen 301 1 introduction most oscillating systems behave like simple harmonic oscillators for su. Determination of halflife period damped oscillations of the gravitational pendulum, etc. In this lab, you will explore the oscillations of a massspring system, with and without damping. Shm basics simple harmonic motion alevel physics youtube.
The damping factor may be controlled with a slider. Introduction if you look to the right, youll see a timelapse photograph of a simple. The simple pendulum is composed of a small spherical ball suspended by a long, light. Damping and forced vibrations are explained in detail, with examples in the real world. Critical damping is important so as to prevent a large number of oscillations and there being too long a time when the system cannot respond to further disturbances. When the motion of an oscillator reduces due to an external force, the oscillator and its motion are damped. A simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in figure 1.
Youll get to see how changing various parameters like the spring constant, the mass, or the amplitude affects the oscillation of the system. The pendulum damped oscillations driven oscillations and resonance. In reality, after numerous oscillations, geo comes to rest. Most physics concepts are expressed equally well in plain english and in equations.
Article pdf available in journal of physics conference series 11573. The damping is proportional to the speed of the pendulum bob. Our experiment may be similar to one you have done in high school, however. Forced oscillation and resonance mit opencourseware. Tape four ceramic magnets to the top of the glider and measure the mass of the glider. A critically damped oscillator, when damped, ceases to oscillate, and returns to its equilibrium position, where it stops moving. We will start with periodic motion for the rst two lectures, with our speci c examples being the motion of a mass attached to the end of a spring, and the pendulum. It is useful because its time period stays the same even when its amplitude changes. Among examples of dissipative forces comprise of friction as well as drag due to movement through liquids and gases. Damped harmonic oscillator physics and astronomy at tamu.
Physics is a quantitative science that uses experimentation and measurement to advance our understanding of the world around us. The motion is regular and repeating, an example of periodic motion. Open the physics with vernier folder and select the file 14 pendulum periods. A summary of simple oscillating systems in s oscillations and simple harmonic motion. Normally, the door would swing back and forth, being damped by friction in the hinges, and air resistance. This driver frequency is in fact the natural frequency of the pendulum.
In the damped case, the torque balance for the torsion pendulum yields the differential equation. Edexcel physics a level unit 5 detailed revision notes thermal physics. Whats the maximum acceleration of the pick head if the amplitude of the oscillation is 5cm. Oscillations of a quadratically damped pendulum naval academy. This laboratory experiment is suitable for undergraduate physics majors taking a first or second course in classical mechanics. After 112 oscillations the amplitude is one half of its original value. Bartons pendulums are used to explain the principles behind resonance. Notes on oscillations and mechanical waves the topics for the second part of our physics class this quarter will be oscillations and waves. You pull the 100 gram mass 6 cm from its equilibrium position and let it go at t 0. Learn exactly what happened in this chapter, scene, or section of oscillations and simple harmonic motion and what it means. The door closer forces the door to stop swinging, and shut immediately. At this simple level we would only deal with two forces gravity and rocket thrust. As and a level practical skills handbook physics a physics b advancing physics this practical skills handbook is designed to accompany the ocr advanced subsidiary gce and advanced gce specifications in physics a and physics b advancing physics for teaching from september 2015. These periodic motions of gradually decreasing amplitude are damped simple harmonic motion.
Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. However, previous studies used theoretical approximations and numerical solutions at a level beyond the. If the mass is not carefully set into motion, it becomes a conical pendulum, which does not swing along a vertical plane and is, therefore, a more complicated physical system. When you hang 100 grams at the end of the spring it stretches 10 cm. The simple pendulum department of physics and astronomy. Pdf damping harmonic oscillator dho for learning media in the. To investigate the relationship between the length of a simple pendulum and the period of its motion. Edexcel as physics revision notes for unit 1 and 2.
The path of periodic motion may be linear, circular. Pendulums a ball of mass 2kg is attached to a string of length 4m, forming a pendulum. Damped oscillations realworld systems have some dissipative forces that decrease the amplitude. Shock absorbers in automobiles and carpet pads are examples of. Each case is given its historical or cultural perspective, a mathematical analysis, and applications. Also shown are the forces on the bob, which result in a net force of toward the equilibrium positionthat is, a restoring force. Characteristics of periodic motion the amplitude, a, is the maximum magnitude of displacement from equilibrium. Shm using phasors uniform circular motion ph i l d l lphysical pendulum example damped harmonic oscillations forced oscillations and resonance. The frequency at which it would oscillate at without the smaller pendulums. However, previous studies used theoretical approximations and numerical solutions at a level beyond the first few university physics courses, with measurements usually limited to the period or amplitude of motion 17. Place a stool under the hanger and measure the initial height x0 above the stool. Simple harmonic motion or shm is the simplest form of oscillatory motion. What distinguishes one system from another is what determines the frequency of the motion.
The pendulm energy model shows a pendulum and associated energy bar charts. The simple pendulum college physics bc open textbooks. A simple pendulum has a smalldiameter bob and a string that has a very small mass but is strong enough not to stretch appreciably. For almost a thousand years, centuries before galileos pendular experiments. Sketch, on a single set of axes, the displacements of a lightly damped and a very heavily damped 3 simple pendulum as a function of time. Finding acceleration the definition for simple harmonic motion tells us that. When a body or a moving particle repeats its motion along a definite path after regular intervals of time, its motion is said to be periodic motion and interval of time is called time or harmonic motion period t.
Oscillation refers to the repeated back and forth movement of something between two positions or states. Its position with respect to time t can be described merely by the angle q. Users can change the initial starting point of the pendulum. Galileos pendulum demo illustrates this if m of string 0 this is a simple pendulum if we have to worry about m of the string or other support, its a physical pendulum 4oct2011 physics 116 au11. Physics simple harmonic motion university of birmingham. Shm arises when force on oscillating body is directly proportional to the displacement from its equilibrium position and at any point of motion, this force is directed towards the equilibrium position. The frequency, f, is the number of cycles per unit time.
Oscillations this striking computergenerated image demonstrates. The mechanical energy of a damped oscillator decreases continuously. Notes on oscillations and mechanical waves periodic motion. The decrease in amplitude is called damping and the motion is called damped oscillation. It also shows how the energy of the pendulum decreases. Add 50 g to the mass hanger and determine the change in position caused by this. Harmonic oscillator part ii physical pendulum experiment 7. In this case the oscillations of the mass of the pendulum are subject to a drag force proportional to the velocity. Calculations and examples with shm scool, the revision. Experiment on damping of a simple harmonic oscillator. Mar 08, 2017 please dont forget to leave a like if you found this helpful.
A numerical study of the forced damped pendulum zhipingyou,ph. Khalsa college, university of delhi, delhi 110 007, india. Asked about the ramifications of his discoveries, hertz replied, nothing, i guess. Experiment 1 the simple pendulum objective to measure the effects of amplitude, mass, and length on the period of a simple pendulum and by graphing to understand which of these parameters matter. The frames of reference in which the experiments are conducted are noninertial. Simple harmonic motion shm is a particular type of oscillation.
You may need several measurements, or measurement strategies, to. The intended audience is the typical undergraduate physics major. Not just a device of pure physics, the pendulum is fascinating because of its. Oscillations of a quadratically damped pendulum iopscience. Its of no use whatsoever this is just an experiment that proves maestro maxwell was rightwe just have these mysterious electromagnetic waves that we cannot see with the naked eye. However, if there is some from of friction, then the amplitude will decrease as a function of time g t a0 a0 x if the damping is sliding friction, fsf constant, then the work done by the. If q is heavily damped the amplitude is much less at its maximum and occurs at a much lower frequency than the natural driver frequency.
Bifurcation analysis of experimental data a thesis. Figure illustrates an oscillator with a small amount of damping. All of the equations above, for displacement, velocity, and acceleration as a function of time, apply to any system undergoing simple harmonic motion. We see from that the net force on the bob is tangent to the arc and equals. Oscillations are happening all around us, from the beating of the human heart, to the vibrating atoms that make up everything.
The laboratory portion of physics 14011501 requires considerable creative input. Examples of simple harmonic motion in everyday life physics. Describe and predict the motion of a damped oscillator under different damping conditions. Simple harmonic motion is a very important type of periodic oscillation where the acceleration.
This animation shows the forces applying to a damped pendulum. The simple pendulum the university of tennessee at. An accurate approximated analytic solution to the nonlinear damped pendulum equation. Lab 11 free, damped, and forced oscillations l1 university of virginia physics department phys 1429, spring 2011 2. For the purposes of this experiment, you will need to ensure that your simple pendulum swings in a vertical plane. Forced vibrations and resonance free vibrations are where the total energy stays the same over time. Isaac physics a project designed to offer support and activities in physics problem solving to teachers and students from gcse level through to university. The system returns to the equilibrium position very slowly, without any oscillation.
Simple harmonic motion scool, the revision website. Periodic motionperiodic motion physics and astronomy at. Lecture notes, lecture all lectures lecture notes from professor alan klein exam 2016, questions and answers, quiz lab 2 this is a lab report for a physics experiment on standing waves lab 3 this is a lab report for a physics experiment on electric field and electric lab for phys 1155 lab 5 this is a lab report for a physics experiment on rc circuits solution manual for investment. An oscillation can be a periodic motion that repeats itself in a regular cycle, such as a sine wavea wave with perpetual motion as in the sidetoside swing of a pendulum, or the upanddown motion of a spring with a weight. Damped oscillations, forced oscillations and resonance. The simple pendulum university of colorado boulder. Cbse ncert notes for class 11 physics oscillations. The simple pendulum deriving the equation of motion the simple pendulum is formed of a light, stiff, inextensible rod of length l with a bob of mass m. A sheet fixed at one end and vibrating at the other end. There is no damping of the motion from friction at the pivot or from air. In this case, dissipative forces are termed to be present to some levels among mechanical systems. The simple pendulum is composed of a small spherical ball suspended by a. The second experiment generated four waves with a wavelength.
Well look at that for two systems, a mass on a spring, and a pendulum. Another factor involved in the period of motion is, the acceleration due to gravity g. Many people are afraid of physics because it relies heavily on mathematics, but dont let this deter you. Physics a level coursework on simple pendulum watch. The apparatus for this experiment consists of a support stand with a string clamp, a small spherical ball with a 125 cm length of light string, a meter stick, a vernier caliper, and a timer. In damped oscillations the amplitude decreases exponentially with time. A simple pendulum consists of a relatively massive object known as the pendulum bob hung by a string from a fixed support. Damped oscillations, forced oscillations and resonance the bible tells you how to go to heaven, not how the heavens go galileo galilei at his trial. Damping, in physics, restraining of vibratory motion, such as mechanical oscillations, noise, and alternating electric currents, by dissipation of energy. Abstract experiments on the oscillatory motion of a suspended bar magnet throws light on the damping e. Emech not constant, oscillations not simple neglect gravity. Calculations and examples with shm scool, the revision website. Lab 1 this is a lab report for a physics experiment on.
This approximation can be applied to topics in many areas of physics. String, pendulum bob, meter stick, computer with uli interface, and a photogate. Introduction a simple pendulum consists of a point mass suspended at the end of a cord of zero mass. Exploring the simple pendulum a bit further, we can discover the conditions under which it performs. Essentially a large pendulum is used to provide a driver frequency which will make the other, smaller pendulums oscillate at the same rate. To study the simple pendulum to examine the physical pendulum to explore damped oscillations to consider driven oscillations and resonance. An example of a damped simple harmonic motion is a simple pendulum. In foucaults experiment, a pendulum of extreme length and precision, free to. Test that the photogate is operational by blocking the sensor with your hand, which should change the gatestate to blocked. In this chapter we will learn about oscillatory motion or oscillations. Alevel physics advancing physicsdamping wikibooks, open. The simple pendulum is a favorite introductory exercise because galileos experiments on pendulums in the early 1600s are usually regarded as the beginning of experimental physics. Thus, avinash et al6 provides a interesting yet cheap method to study the damped pendulum. The frequency and period are reciprocals of each other.
Phy 3 lab 1 the pendulum stony brook physics laboratory. Dumped pendulum lab report 2 introduction in most theoretical analysis of simple harmonic motion, effects associated with dissipative forces are ignored. If you appreciate the help, consider tipping me to keep me going. These, together with experiments on damped motion, enable students to gain comprehensive insights into oscillatory phenomena. We set up and solve using complex exponentials the equation of motion for a damped. Analytic solution to the nonlinear damped pendulum equation. This means that the amplitude of the vibrations remain the same. Find an equation for the position of the mass as a function of time t. As and a level physics a and physics b advancing physics. A case study in physics surveys different types of pendulums. Jul 08, 2002 however, if the angle is large then drag needs to be considered. Experiment 7 physics 4al experiment 6 harmonic oscillator.