SCIED 135 Waves and Optics - Chapter 1 Notes PDF

SCIED 135 Waves and Optics  Assessment Quiz Problem Set Chapter Test Oral Presentation Micro-Demo Term Examinations Problem sets (assignments and seatwork) Strategies Lecture-Discussion Interactive Lecture Demonstration Cooperative Learning Computer Simulate...

SCIED 135 Waves and Optics  Assessment Quiz Problem Set Chapter Test Oral Presentation Micro-Demo Term Examinations Problem sets (assignments and seatwork) Strategies Lecture-Discussion Interactive Lecture Demonstration Cooperative Learning Computer Simulated Experiments PERIODIC MOTION ❑ Explain oscillation using real-life examples ❑ Solve problems involving simple harmonic motion ❑ Discuss examples of SHM in real life. ❑ Calculate the period and/or frequency of a simple and physical pendulum ❑ Identify and explain the different types of damped oscillations. ❑ Demonstrate an appreciation of the different real-life examples of resonance. Elicit Why do dogs walk faster than humans? Does it have anything to do with the characteristics of their legs? Many kinds of motion (such as a pendulum, musical vibrations, and pistons in car engines) repeat themselves. We call such behavior periodic motion or oscillation.  A brief history & contexts The study of SHM started with Galileo’s pendulum experiments (1638) Huygens, Newton & others developed further analyses. pendulum – clocks, seismometers ALL vibrations and waves - sea waves, earthquakes, tides, orbits of planets and moons, water level in a toilet on a windy day, acoustics, AC circuits, electromagnetic waves, vibrations molecular and structural e.g. aircraft fuselage, musical instruments, bridges. A brief history & contexts Periodic Motion/Oscillation - Back and forth motion/repetitive - Sinusoidal - Stable/equilibrium position Periodic Motion/Oscillation WHAT CAUSES PERIODIC MOTION? If a body attached to a spring is displaced from its equilibrium position, the spring exerts a restoring force on it, which tends to restore the object to the equilibrium position. This force causes oscillation of the system, or periodic motion. Describing Oscillation Describing Oscillation  Describing Oscillation The amplitude, A, is the maximum magnitude of displacement from equilibrium. The period, T, is the time for one cycle. The frequency, f, is the number of cycles per unit time. The angular frequency, , is 2π times the frequency:  = 2πf. The frequency and period are reciprocals of each other: f = 1/T and T = 1/f.  Simple Harmonic Motion Careful observation of a big pendulum (PhET) Discuss, in pairs 1.Where is the mass moving fastest, slowest? 2.Where is the mass’s acceleration maximum, zero? 3.Does the time for one complete oscillation depend on the amplitude? 4.What causes the mass to overshoot its equilibrium position? 5.What forces act on the mass? When is the unbalanced force at a maximum value, zero? Do these predictions fit your observations about the acceleration?  Simple Harmonic Motion -any vibrating system where the restoring force is directly proportional to the negative displacement Equilibrium position- where spring exerts no force on the mass (m) Natural state Simple Harmonic Motion Spring stretched Exerts a force to move it back to equilibrium Simple Harmonic Motion Spring compressed Force exerted pushing it back to equilibrium  Simple Harmonic Motion Hooke’s Law When the restoring force is directly proportional to the displacement from equilibrium, the oscillation is called simple harmonic motion.  Simple Harmonic Motion The acceleration The minus sign means the acceleration and displacement always have opposite signs. This acceleration is not constant. A body that undergoes simple harmonic motion is called a harmonic oscillator.  Simple Harmonic Motion Mass-spring system We know that for an ideal spring, the force is related F = −kx to the displacement by. But we just showed that F = −m x 2 harmonic motion has So, we directly find out that k = m 2 the “angular frequency of k motion” of a mass-spring = m system is  Simple Harmonic Motion equations An imaginary circular motion gives a mathematical insight into SHM. Its angular velocity is .. The period and frequency of simple harmonic motion are completely determined by the mass m and the force constant k. In simple harmonic motion, the period and frequency do not depend on the amplitude A.  Simple Harmonic Motion equations.  Simple Harmonic Motion equations Example. Energy in Simple Harmonic Motion Energy in Simple Harmonic Motion Application of Simple Harmonic Motion Vertical SHM Application of Simple Harmonic Motion Example Application of Simple Harmonic Motion Problems 1.  Simple Pendulum Pendulum rides  Simple Pendulum Pendulum rides Simple Pendulum  Simple Pendulum A simple pendulum is an idealized model consisting of a point mass suspended by a massless, unstretchable string.  Physical Pendulum A physical pendulum is any real pendulum that uses an extended body, as contrasted to the idealized model of the simple pendulum with all the mass concentrated at a single point. Sample Problem  Damped Oscillations The decrease in amplitude caused by dissipative forces is called damping, and the corresponding motion is called damped oscillation.  Damped Oscillations Critical damping.-The system no longer oscillates but returns to its equilibrium position without oscillation when it is displaced and released. Overdamping. There is no oscillation, but the system returns to equilibrium more slowly than with critical damping. Underdamping. The system oscillates with steadily decreasing amplitude.  Forced Oscillations and Resonance Damped Oscillation with a Periodic Driving Force -If we apply a periodically varying driving force with angular frequency to a damped harmonic oscillator, the motion that results is called a forced oscillation or a driven oscillation. The amplitude is a function of the driving frequency and reaches a peak at a driving frequency close to the natural frequency of the system. This behavior is called resonance.  Problems 1 2 3 4