Simple harmonic motion mit opencourseware free online. 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. When many oscillators are put together, you get waves. Is independent of amplitude and acceleration due to gravity. In general, any motion that repeats itself at regular intervals is called periodic or harmonic motion. Lecture 30 simple harmonic motionshm msu pa welcome page. We can often observe swinging chandeliers, surging pistons in engines of cars, different pendulums and other similar examples. Lecture 4 simple harmonic motion phys 124h honors analytical physics ib chapter 15 professor noronhahostler. Examples include the motion of the pendulum in a grandfather clock, the vibrations of atom inside a crystal, the oscillations of a buoy due to wave motion in a lake and as we shall discover it forms the. Simple harmonic motion and circular motion chapter 14. Ppt simple harmonic motion powerpoint presentation free. Finding speed, velocity, and displacement from graphs. Write and apply formulas for finding the frequency f, period t, velocity v, or acceleration acceleration ain terms of displacement displacement xor time t.
A simple pendulum has a point mass m on the end of a light inextensible string of length l, which makes an angle. Simple harmonic motion 3 shm description an object is said to be in simple harmonic motion if the following occurs. Harmonic motion refers to the motion an oscillating mass experiences when the restoring force is proportional to the displacement, but in opposite directions. The block on a spring in figure b moves with the same motion.
Shm using phasors uniform circular motion ph i l d l lphysical pendulum example damped harmonic oscillations forced oscillations and resonance. This module is concerned with one of the simplest types of periodic motion1 simple harmonic motion shm. But these are not the only two types of motion we can observe in every day life. Simple harmonic oscillators 1 introduction the simplest thing that can happen in the physical universe is nothing. Describe the motion of pendulums pendulums and calculate the length required to produce a given frequency. This lecture is a must hookes law springs simple harmonic motion pendulums great demos. Ag f when f is removed then there will be an extra upward buoyant force. When \\gamma 2\omega\, the system is said to be critically damped. Physics i lecture 11 simple harmonic motion author. The displacement of the damped oscillator over time is simple harmonic motion with a continually decreasing amplitude.
The characteristic equation for shm is a cosine function. Periodic or near periodic motion is one of the fundamental ways how bodies can move. Periodic motion we call a motion periodic if the state of a system repeats itself after regular time intervals. Examples of periodic motion can be found almost anywhere. Important insight into figure a shows a shadow movie of a ball made by projecting a light past the ball and onto a screen. Resonance examples and discussion music structural and mechanical engineering waves sample problems.
Complete solution to the harmonically driven oscillator lecture 5. The force is always opposite in direction to the displacement direction. The second half of the lecture is an introduction to the nature and behavior of waves. Lecture 30 simple harmonic motionshm simple harmonic is the simplest model possible of oscillatory motion, yet it is extremely important. Phys 200 lecture 17 simple harmonic motion open yale. The angular frequency and period do not depend on the amplitude of oscillation. Simple harmonic motion vibration oscillation toandfro repeating movement simple harmonic motion s. List the characteristics of simple harmonic motion. Overview of key terms, equations, and skills for simple harmonic motion. 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.
Resonance examples and discussion music structural and mechanical engineering. A mechanical example of simple harmonic motion is illustrated in the following diagrams. A v max,2 v max,1 b v max,2 2v max,1 c v max,2 4v max,1 checkpoint k m. Lecture notes physics i physics mit opencourseware. Harmonically driven damped harmonic oscillator lecture 4. The focus of the lecture is simple harmonic motion. Physics 1 simple harmonic motion introduction to simple harmonic motion.
Physics 106 lecture 12 oscillations ii sj 7th ed chap 15. Perhaps the simplest mechanical system whose motion follows a linear differential equation with constant coefficients is a mass on a spring. A special kind of oscillation exploring the acceleration. A simple harmonic oscillator can be described mathematically by. The next simplest thing, which doesnt get too far away from nothing, is an oscillation about nothing. Introducing data studio one dimensional motion, velocity and acceleration hour two problem solving session 1. Energy of the harmonic oscillator the total mechanical energy of a simple harmonic oscillator is a constant of the motion and is proportional to the square of the amplitude. Examples include the motion of the pendulum in a grandfather clock, the vibrations of atom inside a crystal, the oscillations of a buoy due to wave motion in a lake. Simple harmonic motion or shm is the simplest form of oscillatory motion. Problems are introduced and solved to explore various aspects of oscillation. Feb 07, 2015 this lecture is a must hookes law springs simple harmonic motion pendulums great demos. We do that before considering the lightly damped oscillator because the mathematics is a little more. The wave equation, solutions to the wave equation lecture 8.
How are the maximum veloci7es in the two cases related. In this lecture, we will be looking at a wide variety of oscillatory phenomena. Wolfson and pasachoff, physics with modern physics, chapter 15. Lecture notes physics iii physics mit opencourseware. 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. After a brief recap of undamped simple harmonic motion, we go on to look at a heavily damped oscillator. Pdf this chapter is intended to convey the basic concepts of oscillations. Simple harmonic motionsimple harmonic motion no forcing, and no. A free powerpoint ppt presentation displayed as a flash slide show on id. This lecture continues the topic of harmonic motions. Shm occurs when a particle or body is displaced from an equilibrium position and experiences a restoring force i. An example of this is a weight bouncing on a spring. Shm occurs when a particle or body is displaced from an equilibrium position and experiences a restoring.
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