Simple Harmonic Motion And Waves 17
AP PHYSICSUnit 5: Simple Harmonic Motion and Waves
SIMPLE HARMONIC MOTION AND WAVESThe following slides introduce you to SHM andWaves and provide practice problems withsolutions. The slides are ordered so that you review period,frequency and Hooke’s Law and then move intoexploring energy and periods of Mass-springsystems and pendulums. Then mechanical waves, such as sound, areintroduced and the nature of waves is explored.
SCHEDULE FOR SHMMonday-Wednesday: New content Thursday-Friday: Practice Monday: Quiz Tuesday: Start Mechanical Waves * Note: We can still finish all the content for theyear, but we need to pick up the pace a little.
OBJECTIVES What is periodic motion? Period and frequencyHooke’s Law reviewWhat is simple harmonic motion? How do we model SHM using equations? Mass- spring systems and pendulums What is a wave? How is it similar to SHM (sinusoidal nature of waves)?What are the properties of waves? Energy and period quantificationsWhat is a transverse and a longitudinal wave?How do we quantify wave properties?How do we model wave behavior through equations?
DAY 1Intro to Simple Harmonic Motion
THINGS THAT UNDERGO SHMMass bobbing vertically from a spring w/ no air resistance Mass on a frictionless floor attached to a spring on thewall Simple pendulum or person on a swing where maxdisplacement is not excessive A person who jumps into a tunnel that goes clear throughthe center of the Earth all the way to the opposite side All of these situations have common features: periodic motion with constant period an equilibrium point half way between its high and low (or leftmost andrightmost) points where its moving its fastest a constant amplitude that is half of its total span (from high to low) a “restoring force” that always acts in the direction of equilibrium and is a maxat the extremes (max distance from equil.) [Note: Not necessarily periodicmotion]
What is SHM?
PRACTICEA large pearl was found in the Philippines in 1934. Supposethe pearl is placed on a spring scale whose spring constant is362 N/m. If the scale’s platform oscillates with a frequency of1.20 Hz, what is the mass of the pearl?Given:k 362 N/mf 1.20 HzUnknown:m ?Use the equation for the period of amass-spring system. Then express theperiod in terms of frequency (T 1/f).m 1T 2p kf362 N/mkm 6.37 kg2 2224p f4p (1.20 Hz)
PROBLEM 2The antennae of male mosquitoes have many hairs thatreceive sound signals from female mosquitoes. Femalemosquitoes emit a frequency of about 230 Hz. Suppose amass is attached to a spring with a spring constant of1.14x104 N/m. How large is the mass if its oscillationfrequency is the same as a mosquito’s?Given:f 230 Hzk 1.14 104 N/mUnknown:m ?
PROBLEM 2 SOLUTIONUse the equation for the period of a mass-spring system tosolve for m:
Waves and provide practice problems with solutions. The slides are ordered so that you review period, frequency and Hooke’s Law and then move into exploring energy and periods of Mass-spring systems and pendulums. Then mechanical waves, such as sound, are introduced and the nature of waves is explored.
Lesson 14: Simple harmonic motion, Waves (Sections 10.6-11.9) Lesson 14, page 1 Circular Motion and Simple Harmonic Motion The projection of uniform circular motion along any axis (the x-axis here) is the same as simple harmonic motion. We use our understanding of uniform circular motion to arrive at the equations of simple harmonic motion.
Simple Harmonic Motion The motion of a vibrating mass-spring system is an example of simple harmonic motion. Simple harmonic motion describes any periodic motion that is the result of a restoring force that is proportional to displacement. Because simple harmonic motion involves a restoring force, every simple harmonic motion is a back-
Chapter 11: Harmonic Motion 170 Learning Goals In this chapter, you will: DLearn about harmonic motion and how it is fundamental to understanding natural processes. DUse harmonic motion to keep accurate time using a pendulum. DLearn how to interpret and make graphs of harmonic motion. DConstruct simple oscillators.
Simple Harmonic Motion, SHM Simple harmonic motion . Simple harmonic motion is periodic motion in the absence of friction and produced by a restoring force that is directly proportional to the displacement and oppositely directed. A restoring force, F, acts in the direction opposite the displacement of the oscillating body. F - kx. A .
AP Physics 1- Simple Harmonic Motion and Waves Practice Problems FACT: Simple harmonic motion (SHM) refers to the back-an-forth oscillation of an object, such as a mass on a spring and a pendulum. The position as a function of time graph is sinusoidal. SHM and uniform circular motion (UCM) are closely related, in fact, SHM describes the one .
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). An ideal spring obeys Hooke’s law, so the restoring force is F x –kx, which results in simple harmonic motion.
SHM. Whereas, the oscillatory motion of a simple pendulum is a SHM, and since it repeats the motion in definite intervals of time called the period, T, it a periodic motion. The precise definition of a simple harmonic motion is that the net force, !⃗ on the simple harmonic oscillator has a magnitude that is
indicates simple harmonic motion, since independence of the period from the amplitude is what distinguishes simple harmonic motion from other types of harmonic motion. 2. Period and Mass. Mass (g) t1 (sec) t2 (sec) Period (sec) 35.0 1.814 2.290 0.476 45.0 3.116 3.705 0.589 55.0 2.150 2.755 0.605 70.0 1.217 1.889 0.672
