1. Objectives: 1)Describe how energy and speed vary in simple harmonic motion 2) Calculate sinusoidal wave properties in terms of amplitude, wavelength, frequency, and period. 3) Identify different types of waves. Objectives: 1)Describe how energy and speed vary in simple harmonic motion 2) Calculate sinusoidal wave properties in terms of amplitude, wavelength, frequency, and period. 3) Identify different types of waves.

2. 1.A paper airplane accumulates 0.80 x 10 -12 C of charge while flying perpendicular to Earth’s magnetic field of 5.0 x 10 -5 T. How fast is the paper airplane flying, neglecting air resistance, if the magnetic force acting on it is 6.4 x 10 -16 N? **F=qvBsin  ** 2.What is the direction of the force on a positive charge that travels through a magnetic field as shown below? 1.A paper airplane accumulates 0.80 x 10 -12 C of charge while flying perpendicular to Earth’s magnetic field of 5.0 x 10 -5 T. How fast is the paper airplane flying, neglecting air resistance, if the magnetic force acting on it is 6.4 x 10 -16 N? **F=qvBsin  ** 2.What is the direction of the force on a positive charge that travels through a magnetic field as shown below? SN

3. 1. 6.4 x 10 -16 N=(0.8x10 -12 C)(v)(5.0 x 10 -5 T)(sin90 o ) v = 6.4 x 10 -16 = 16 m/s (0.8x10 -12 )(5.0x10 -5 )(sin90 o ) 2. The index finger points in the direction of motion, the other fingers north to south in the direction of the magnetic field, leaving the thumb, showing the direction of the force pointing into the page, or “downwards” or negative z. 1. 6.4 x 10 -16 N=(0.8x10 -12 C)(v)(5.0 x 10 -5 T)(sin90 o ) v = 6.4 x 10 -16 = 16 m/s (0.8x10 -12 )(5.0x10 -5 )(sin90 o ) 2. The index finger points in the direction of motion, the other fingers north to south in the direction of the magnetic field, leaving the thumb, showing the direction of the force pointing into the page, or “downwards” or negative z.

6. SHM: The motion of an oscillating object which experiences a displacement and a restoring force Displacement,  x: the distance of an object from its equilibrium position SHM: The motion of an oscillating object which experiences a displacement and a restoring force Displacement,  x: the distance of an object from its equilibrium position

7. Amplitude,  A: the magnitude of the maximum displacement of an object from its equilibrium position Period, T: The time for one complete cycle of motion Frequency, f: the number of cycles per second. Amplitude,  A: the magnitude of the maximum displacement of an object from its equilibrium position Period, T: The time for one complete cycle of motion Frequency, f: the number of cycles per second.

8. A wave is defined as the transfer of energy from one point to another Total Energy = Potential Energy + Kinetic Energy Mechanical waves require a medium for the transfer of energy to occur Non-mechanical waves do not require a medium for the transfer of energy to occur A wave is defined as the transfer of energy from one point to another Total Energy = Potential Energy + Kinetic Energy Mechanical waves require a medium for the transfer of energy to occur Non-mechanical waves do not require a medium for the transfer of energy to occur

9. E total = KE + PE or E = K + U Consider the case of a block of mass m attached to a massless spring. As the block oscillates (without friction), the spring provides the restorative force that moves it from + x to – x. E total = KE + PE or E = K + U Consider the case of a block of mass m attached to a massless spring. As the block oscillates (without friction), the spring provides the restorative force that moves it from + x to – x.

11. Such springs are said to follow Hooke's Law. F spring = k * x where k is the spring constant and x is the amount of stretch or compression. If a spring is not stretched or compressed, then there is no elastic potential energy stored in it. The spring is said to be at its equilibrium position. The equilibrium position is the position that the spring naturally assumes when there is no force applied to it. Such springs are said to follow Hooke's Law. F spring = k * x where k is the spring constant and x is the amount of stretch or compression. If a spring is not stretched or compressed, then there is no elastic potential energy stored in it. The spring is said to be at its equilibrium position. The equilibrium position is the position that the spring naturally assumes when there is no force applied to it.

12. The amount of elastic potential energy is related to the amount of stretch (or compression) and the spring constant. The equation is

13. Where k is the spring constant and x is the stretch or compression distance from the equilibrium position

14. Calculating Energy in SHMCalculating Energy in SHM KE = ½ mv 2 and PE = ½ kx 2 So that at the maximum displacement,  x=  A, or the amplitude, it’s instantaneous velocity is 0. E total = ½ m(0) 2 + ½k(  A) 2 = ½k(  A) 2 The total energy of an object in SHM is directly proportional to the square of the amplitude KE = ½ mv 2 and PE = ½ kx 2 So that at the maximum displacement,  x=  A, or the amplitude, it’s instantaneous velocity is 0. E total = ½ m(0) 2 + ½k(  A) 2 = ½k(  A) 2 The total energy of an object in SHM is directly proportional to the square of the amplitude

15. Velocity of the oscillating object is a function of the position ½k(  A) 2 = ½ mv 2 + ½ kx 2. Solving for v allows us to find the velocity anywhere along the path Velocity of the oscillating object is a function of the position ½k(  A) 2 = ½ mv 2 + ½ kx 2. Solving for v allows us to find the velocity anywhere along the path

17. Please sketch the problem, identify the given information, and write the formula you choose to solve each problem.

19. 1.The wavelength of the wave in the diagram above is given by letter ______. 2. The amplitude of the wave in the diagram above is given by letter _____. 3. Indicate the interval which represents one full wavelength. 1.The wavelength of the wave in the diagram above is given by letter ______. 2. The amplitude of the wave in the diagram above is given by letter _____. 3. Indicate the interval which represents one full wavelength.

20. An object in orbit also travels from + A to –A

21. SHM is described by a sinusoidal function of time where ω is the angular speed of the object (in rad/s), or angular frequency, since ω = 2  f y =  A sinθ(2  f)t =  A sin θ(2  /T)t The period of motion is given by or for a pendulum where k is the spring force constant The frequency and the angular velocity are then SHM is described by a sinusoidal function of time where ω is the angular speed of the object (in rad/s), or angular frequency, since ω = 2  f y =  A sinθ(2  f)t =  A sin θ(2  /T)t The period of motion is given by or for a pendulum where k is the spring force constant The frequency and the angular velocity are then

22. The velocity of an object in simple harmonic motion is: and the acceleration: Note that the acceleration is not constant—the equations of motion for constant acceleration cannot be used here. The velocity of an object in simple harmonic motion is: and the acceleration: Note that the acceleration is not constant—the equations of motion for constant acceleration cannot be used here. θ θ

23. Amplitude, A : the height of a wave crest or trough Wavelength, : the distance between two successive troughs (or crests) Frequency, f: the number of cycles, or wavelengths, that pass by a given point per second Period, T: The time for one complete wavelength to pass by a given point Wave speed, v (nu): The distance a wave travels in a time of one period, T Amplitude, A : the height of a wave crest or trough Wavelength, : the distance between two successive troughs (or crests) Frequency, f: the number of cycles, or wavelengths, that pass by a given point per second Period, T: The time for one complete wavelength to pass by a given point Wave speed, v (nu): The distance a wave travels in a time of one period, T

24.  Mechanical: Travel through a medium (like sound waves or earthquakes)  Nonmechanical: Do not require a medium (like electromagnetic waves) Transverse Longitudinal Elliptical Torsional  Mechanical: Travel through a medium (like sound waves or earthquakes)  Nonmechanical: Do not require a medium (like electromagnetic waves) Transverse Longitudinal Elliptical Torsional

25. Types of waves http://dev.physicslab.org/DocumentPrint.aspx ?doctype=3&filename=WavesSound_Introduc tionWaves.xml Tacoma Narrows Bridge Collapse http://dev.physicslab.org/DocumentPrint.aspx ?doctype=3&filename=WavesSound_Introduc tionWaves.xml http://video.google.com/videoplay?docid=40 87615334344625698#docid=2260354895340 450887 http://video.google.com/videoplay?docid=40 87615334344625698#docid=2260354895340 450887 Types of waves http://dev.physicslab.org/DocumentPrint.aspx ?doctype=3&filename=WavesSound_Introduc tionWaves.xml Tacoma Narrows Bridge Collapse http://dev.physicslab.org/DocumentPrint.aspx ?doctype=3&filename=WavesSound_Introduc tionWaves.xml http://video.google.com/videoplay?docid=40 87615334344625698#docid=2260354895340 450887 http://video.google.com/videoplay?docid=40 87615334344625698#docid=2260354895340 450887