2 Periodic Motion A repeated motion is called periodic motion What are some examples of periodic motion?The motion of Earth orbiting the sunA child swinging on a swingPendulum of a grandfather clock
3 Simple Harmonic Motion Simple harmonic motion is a form of periodic motionThe conditions for simple harmonic motion are as follows:The object oscillates about an equilibrium positionThe motion involves a restoring force that is proportional to the displacement from equilibriumThe motion is back and forth over the same path
4 Earth’s OrbitIs the motion of the Earth orbiting the sun simple harmonic?NOWhy not?The Earth does not orbit about an equilibrium position
5 p. 438 of your bookThe spring is stretched away from the equilibrium positionSince the spring is being stretched toward the right, the spring’s restoring force pulls to the left so the acceleration is also to the left
6 p. 438 of your bookWhen the spring is unstretched the force and acceleration are zero, but the velocity is maximum
7 p.438 of your bookThe spring is stretched away from the equilibrium positionSince the spring is being stretched toward the left, the spring’s restoring force pulls to the right so the acceleration is also to the right
8 DampingIn the real world, friction eventually causes the mass-spring system to stop movingThis effect is called damping
9 Mass-Spring DemoI suggest you play around with this demo…it might be really helpful!
10 Hooke’s LawThe spring force always pushes or pulls the mass back toward its original equilibrium positionMeasurements show that the restoring force is directly proportional to the displacement of the mass
11 Hooke’s Law Felastic= Spring force k is the spring constant x is the displacement from equilibriumThe negative sign shows that the direction of F is always opposite the mass’ displacement
12 FlashbackAnybody remember where we’ve seen the spring constant (k) before?PEelastic = ½kx2A stretched or compressed spring has elastic potential energy!!
13 Spring ConstantThe value of the spring constant is a measure of the stiffness of the springThe bigger k is, the greater force needed to stretch or compress the springThe units of k are N/m (Newtons/meter)
14 Sample Problem p.441 #2A load of 45 N attached to a spring that is hanging vertically stretches the spring 0.14 m. What is the spring constant?
15 Solving the Problem Why do I make x negative? Because the displacement is down
16 Follow Up QuestionWhat is the elastic potential energy stored in the spring when it is stretched 0.14 m?
17 The simple pendulum The simple pendulum is a mass attached to a string The motion is simple harmonicbecause the restoring force is proportional to the displacement and because the mass oscillates about an equilibrium position
18 Simple Pendulum The restoring force is a component of the mass’ weight As the displacement increases, the gravitational potential energy increases
19 Simple Pendulum Activity You should also play around with this activity to help your understanding
20 Comparison between pendulum and mass-spring system (p. 445)
22 Amplitude of SHMAmplitude is the maximum displacement from equilibriumThe more energy the system has, the higher the amplitude will be
23 Period of a pendulumT = periodL= length of stringg= 9.81 m/s2
24 Period of the PendulumThe period of a pendulum only depends on the length of the string and the acceleration due to gravityIn other words, changing the mass of the pendulum has no effect on its period!!
25 Sample Problem p. 449 #2You are designing a pendulum clock to have a period of 1.0 s. How long should the pendulum be?
31 Day 2: Properties of Waves A wave is the motion of a disturbanceWaves transfer energy by transferring the motion of matter instead of transferring matter itselfA medium is the material through which a disturbance travelsWhat are some examples of mediums?WaterAir
32 Two kinds of Waves Mechanical Waves require a material medium i.e. Sound wavesElectromagnetic Waves do not require a material mediumi.e. x-rays, gamma rays, etc
33 Pulse Wave vs Periodic Wave A pulse wave is a single, non periodic disturbanceA periodic wave is produced by periodic motionTogether, single pulses form a periodic wave
34 Transverse WavesTransverse Wave: The particles move perpendicular to the wave’s motionParticles move iny directionWave moves inX direction
35 Longitudinal (Compressional) Wave Longitudinal (Compressional) Waves: Particles move in same direction as wave motion (Like a Slinky)
36 Longitudinal (Compressional) Wave Crests: Regions of High Density becauseThe coils are compressedTroughs: Areas of Low Density becauseThe coils are stretched
37 Wave SpeedThe speed of a wave is the product of its frequency times its wavelengthf is frequency (Hz)λ (lambda) Is wavelength (m)
38 Sample Problem p.457 #4A tuning fork produces a sound with a frequency of 256 Hz and a wavelength in air of 1.35 ma. What value does this give for the speed of sound in air?b. What would be the wavelength of the wave produced b this tuning fork in water in which sound travels at 1500 m/s?
41 Wave InterferenceSince waves are not matter, they can occupy the same space at the same timeThe combination of two overlapping waves is called superposition
42 The Superposition Principle The superposition principle: When two or more waves occupy the same space at the same time, the resultant wave is the vector sum of the individual waves
43 Constructive Interference (p.460) When two waves are traveling in the same direction, constructive interference occurs and the resultant wave is larger than the original waves
44 Destructive Interference When two waves are traveling on opposite sides of equilibrium, destructive interference occurs and the resultant wave is smaller than the two original waves
45 ReflectionWhen the motion of a wave reaches a boundary, its motion is changedThere are two types of boundariesFixed BoundaryFree Boundary
46 Free Boundaries A free boundary is able to move with the wave’s motion At a free boundary, the wave is reflected
47 Fixed BoundariesA fixed boundary does not move with the wave’s motion (pp. 462 for more explanation)Consequently, the wave is reflected and inverted
48 Standing WavesWhen two waves with the same properties (amplitude, frequency, etc) travel in opposite directions and interfere, they create a standing wave.
49 Standing Waves A N N A A N Standing waves have nodes and antinodes Nodes: The points where the two waves cancelAntinodes: The places where the largest amplitude occursThere is always one more node than antinodeANANAN
50 Sample Problem p.465 #2A string is rigidly attached to a post at one end. Several pulses of amplitude 0.15 m sent down the string are reflected at the post and travel back down the string without a loss of amplitude. What is the amplitude at a point on the string where the maximum displacement points of two pulses cross? What type of interference is this?
51 Solving the Problem What type of boundary is involved here? FixedSo that means the pulse will be reflected and invertedWhat happens when two pulses meet and one is inverted?Destructive interferenceThe resultant amplitude is 0.0 m
52 Helpful SimulationsMass-Spring system:Pendulum:Wave on a string system: