This lecture continues the topic of harmonic motions. Simple harmonic motion simple harmonic motion arises when we consider the motion of a particle whose acceleration points towards a fixed point o and is proportional to the distance of the particle from o so the acceleration increases as the distance from the fixed point increases. Here we finally return to talking about waves and vibrations, and we start off by rederiving the general solution for simple harmonic motion. Both longitudinal and transverse waves are defined and. Is independent of amplitude and acceleration due to gravity. Frictional forces will diminish the amplitude of oscillation until eventually the system is at rest. Oscillatory motion is defined as the to and fro motion of the pendulum in a periodic fashion and the centre point of oscillation known as equilibrium position. Simple harmonic motion shm follows logically on from linear motion and circular motion. Damped simple harmonic motion pure simple harmonic motion1 is a sinusoidal motion, which is a theoretical form of motion since in all practical circumstances there is an element of friction or damping. A springblock system is the simplest example of simple harmonic motion. Quantum physics ii, lecture notes 6 mit opencourseware. Simple harmonic motion if a particle repeats its motion about a fixed point after a regular time interval in such a way that at any moment the acceleration of the particle is directly proportional to its displacement from the fixed point at that moment and is always directed towards the fixed point, then the motion of the particle is called simple harmonic motion.
Periodic motion is the motion in which an object repeats its path in equal intervals of time. Dec 26, 2014 an object in simple harmonic motion has the same motion as of an object in uniform circular motion. To derive the equation for position in shm, we start by comparing simple harmonic motion to circular motion. 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. Mar 24, 2016 for the love of physics walter lewin may 16, 2011 duration. The simple harmonic motion of a mass on a spring is an example of an energy transformation between potential energy and kinetic energy. The time interval of each complete vibration is the same, and. Equation 11 gives acceleration of particle executing simple harmonic motion and quantity. Simple harmonic motion is the simplest example of oscillatory motion. When an object moves to and fro along a straight line, it performs the simple harmonic motion. 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. Dynamics problems involving newtons second law of motion often involve second order linear differential equations as illustrated in the derivation of equation 1 for a particle attached to a light spring. Simple harmonic motion and damping georgia tech ece. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration.
Simple harmonic motion shm simple harmonic oscillator sho when the restoring force is directly proportional to the displacement from equilibrium, the resulting motion is called simple harmonic motion shm. Consider displacing the spring an amount x from the new equilibrium. Aug 31, 2012 here we finally return to talking about waves and vibrations, and we start off by rederiving the general solution for simple harmonic motion using complex numbers and differential equations. Pdf chapter simple harmonic motion idowu itiola academia. Shm using phasors uniform circular motion ph i l d l lphysical pendulum example damped harmonic oscillations forced oscillations and resonance.
They also fit the criteria that the bobs velocity is maximum as it passes through equilibrium and its acceleration is minimal while at each endpoint. 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. Abstract modeling the motion of the simple harmonic pendulum from newtons second law, then comparing this with the small angle approximation model using matlab. The mass is attached by a string to the support, to form a simple pendulum. For an understanding of simple harmonic motion it is. Physics 106 lecture 12 oscillations ii sj 7th ed chap 15. Simple harmonic motion problems with answers final copy. Simple harmonic motion example problems with solutions pdf. Learn exactly what happened in this chapter, scene, or section of oscillations and simple harmonic motion and what it means.
Deriving equation of simple harmonic motion physics forums. Problems are introduced and solved to explore various aspects of oscillation. Simple harmonic motion is something that can be described by a trigonometric function like this. In the example below, it is assumed that 2 joules of work has been done to set the mass in motion. Simple harmonic motion occurs when the restoring force is proportional to the displacement. All examples of oscillatory motion are the examples of simple harmonic motion. The motion is sinusoidal in time and demonstrates a single resonant frequency.
The second half of the lecture is an introduction to the nature and behavior of waves. For the love of physics walter lewin may 16, 2011 duration. To determine if the motion is simple harmonic, we need to see if the restoring force. An harmonic oscillator is a particle subject to a restoring force that is proportional to the displacement of the particle. In the second short derivation of xt we presented above, we guessed a solution.
Consider the particle in uniform circular motion with radius a and angle. It is one of the more demanding topics of advanced physics. Simple harmonic motion or shm is the simplest form of oscillatory motion. Phys 200 lecture 17 simple harmonic motion open yale. Having established the basics of oscillations, we now turn to the special case of simple harmonic motion. Resonance examples and discussion music structural and mechanical engineering waves sample problems.
Simple harmonic motion can serve as a mathematical model for a variety of motions, such as the oscillation of a spring. The corresponding motion is called damped oscillations. The student can perform data analysis and evaluation of evidence. Using n2l suppose you add a mass m to the end of a suspended vertical spring. Shm as projection of uniform circular motion youtube. The topic is quite mathematical for many students mostly algebra, some trigonometry so the pace might have to be judged accordingly. Simple harmonic motion, in physics, repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by hookes law. The simple harmonic pendulum joel ballard spring 2012. Relation between uniform circular motion and shm 26. Trouble with equation of motion for a damped pendulum. You may be asked to prove that a particle moves with simple harmonic motion.
When you hang 100 grams at the end of the spring it stretches 10 cm. Equation of shmvelocity and accelerationsimple harmonic. An account is given for the simplest kind of oscil latory motion, due to a linear restoring force and without dissipation. We begin by defining the displacement to be the arc length. With the free motion equation, there are generally two bits of information one must have to appropriately describe the masss motion. Notes for school exams physics xi simple harmonic motion. The motion of a simple pendulum is a great example of simple harmonic motion. A particle which moves under simple harmonic motion will have the equation w 2 x. It gives you opportunities to revisit many aspects of physics that have been covered earlier. Download simple harmonic motion problems with answers final copy. Independence of period and amplitude in simple harmonic motion. We need to know what periodic motion is to understand simple harmonic motion.
Analyze the motion of a body to determine if it can be described either exactly or approximately in terms of simple harmonic motion and identify the conditions under which approximations to simple harmonic motion are valid. We will now derive the simple harmonic motion equation of a pendulum from newtons second law. Dec 27, 2011 simple harmonic motion occurs when the restoring force is proportional to the displacement. The mass displaces the spring an amount x1 from equilibrium. The topic is quite mathematical for many students mostly algebra, some trigonometry so the pace might have to be judged. Harmonic motion part 3 no calculus video khan academy. Simple harmonic motion shm is caused by a restoring force. With this dissipating forces present, the oscillations are noted as damped harmonic motion rather than simple harmonic motion, where energy and amplitude are always constant. Imagine that the mass was put in a liquid like molasses. Derivation of simple harmonic motion equation stack exchange. Simple harmonic motion let us again consider the springmass system lies on a.
We see from that the net force on the bob is tangent to the arc and equals. A mechanical example of simple harmonic motion is illustrated in the following diagrams. Oscillations and simple harmonic motion sparknotes. Simple harmonic motion differential equations youtube. When an object moves to and fro along a line, the motion is called simple harmonic motion. The focus of the lecture is simple harmonic motion.
A summary of simple harmonic motion in s oscillations and simple harmonic motion. Damping is when the amplitude of oscillations decreases because of dissipative forces. For an understanding of simple harmonic motion it is sufficient to investigate the solution of. We are looking for a position function xt such that the second time derivative position function is proportional to. Professor shankar gives several examples of physical systems, such as a mass m attached to a spring, and explains what happens when such systems are disturbed. In classical physics this means f mam 2 x aaaaaaaaaaaaa t2 kx. The above equation is known to describe simple harmonic motion or free motion.
Simple pendulum time period, derivation, and physical. It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by t. Harmonic motion part 3 no calculus this is the currently selected item. F ma acceleration due to gravity will be a function of. When we swing a simple pendulum, it moves away from its mean equilibrium position. This oer repository is a collection of free resources provided by equella. We know that in reality, a spring wont oscillate for ever. In the simplest application, the classical harmonic oscillator arises when a mass m free to move along the x axis is attached to a spring with spring constant k. And it just oscillates back and forth, back and forth. Simple harmonic motion can be described as an oscillatory motion in which the acceleration of the particle at any position is directly proportional to the displacement from the mean position. Chapter simple harmonic motion we are to admit no more causes of. A motion that repeats itself in equal intervals of time is periodic.
Modeling the motion of the simple harmonic pendulum from newtons second law, then comparing this with the small angle approximation model using mat. A mass m 100 gms is attached at the end of a light spring which oscillates on a friction less horizontal table with an amplitude equal to 0. We will describe the conditions of a simple harmonic oscillator, derive its resultant motion, and finally derive the energy of such a system. Harmonic oscillator assuming there are no other forces acting on the system we have what is known as a harmonic oscillator or also known as the springmassdashpot. We will now add frictional forces to the mass and spring. You pull the 100 gram mass 6 cm from its equilibrium position and. Simple harmonic oscillator yt kt yt kt y t ky t k k m sin and cos. Ordinary differential equationssimple harmonic motion. Shm occurs when a particle or body is displaced from an equilibrium position and experiences a restoring force i.
Simple pendulums are sometimes used as an example of simple harmonic motion, shm, since their motion is periodic. A simple pendulum is an idealized model consisting of a. In general, the name displacement is given to a physical quantity which undergoes a change with time in a periodic motion. Lets derive the force law for simple harmonic motion with an example. One such complete motion is known as an oscillation. An object in simple harmonic motion has the same motion as of an object in uniform circular motion. And just so you know i know i put the label harmonic motion on all of these this is simple harmonic motion. Resonance examples and discussion music structural and mechanical engineering. Oscillations of a pendulum are an example of simple harmonic motion. An ideal spring obeys hookes law, so the restoring force is f x kx, which results in simple harmonic motion. When we swing it, it moves to and fro along the same line. During a landing, an astronaut and seat had a combined mass of 80.