Lecture 25 Announcements Simple harmonic motion 1 Demo weight on spring 2 3 4 Exam 4 results a Exams can be picked up in the normal boxes b Last page not yet graded TA got them yesterday Final exam info a Take in Testing Center any time during Finals week b Four hour time limit 1 2 point after 4 05 c No calculator no note card d The first page of final with list of equations will be posted to the class website soon e I plan approx 40 questions i approx 10 on new stuff Chap 13 14 ii approx 30 on Chapters 1 12 f Last year s exam posted to website i 71 average 76 median 2 hour ave time Clicker quiz Class survey vote for an option a Final will count 20 of grade as in syllabus b Final will count 20 of grade plus it will replace your lowest midterm exam score if higher 11 of grade i but will be a little more difficult than last year s exam Instructor course evaluations due before Dec 13 http studentratings byu edu Please take both the ratings and the comments seriously Sinusoidal vibrations Occurs when an object has a spring like restoring force F displacement Result x Acos t or x Asin t or x Acos t what s the difference A amplitude how far from origin it travels x t v t a t Colton Lecture 25 12 2 08 pg 1 Colton Lecture 25 12 2 08 pg 2 Quick proof using simple calculus sorry Start with F x A x B C 1 0 0 5 0 5 2 4 6 8 10 t 1 0 Reading info from graph x Clicker quiz 1 Where does it have the most kinetic energy a position A b position B c position C 1 0 0 5 0 5 2 4 6 8 10 t Clicker quiz 2 Where does it have the most potential energy a position A b position B c position C 1 0 Amplitude A Period T sec Frequency f cycles sec Hz Angular frequency rad sec Angular frequency Where s the angle Demo SHM Circular motion analogy Colton Lecture 25 12 2 08 pg 3 f 2 Clicker quiz 3 Where does it have the largest acceleration a position A b position B c position C Colton Lecture 25 12 2 08 pg 4 Clicker quiz Given the oscillation picture below Springs Demo spring with mass Frequency period Pendulums Demo pendulum what s the correct equation to describe the position vs time a x t 6 cos t b x t 3 sin 2t c x t 6 sin 2t d x t 3 sin t e x t 3 cos t Frequency period Clicker quiz Does period depend on amplitude a yes b no c it depends Colton Lecture 25 12 2 08 pg 5 Colton Lecture 25 12 2 08 pg 6 Worked Problem A 70 kg trapeze artist swings on a long trapeze and takes 5 seconds to return to his starting spot How long will it take a woman of mass 50kg to make the same swing sec Oscillating motion that transfers energy but not mass Direction where the energy is going Medium what is doing the waving How long will it take for the 70 kg man to swing from his starting place to when he first reaches the bottom sec Oscillation how the medium is moving Transverse Oscillation is to the direction of the wave Longitudinal Oscillation is to the direction of the wave Web Demo http www gmi edu drussell Demos waves wavemotion html How long is the rope m Colton Lecture 25 12 2 08 pg 7 Examples Slinky demo Rope demo Shive wave machine demo Sound Earthquake P S Water Light Colton Lecture 25 12 2 08 pg 8 surface of the Sun Wikipedia S wave spherical Reflections Superposition Interference Clicker quiz What happens when an upward pulse hits the end and turns around a the wave reflects back upward b the wave reflects back downward c it depends Clicker quiz What happens if two pulses one from each end meet in the middle Do they pass through or reflect back when they meet a pass through b reflect off of each other What about this case Web Demo http www colorado edu physics phet simulations stringwave stringWave swf Boundaries Rope Light rope meets heavy rope Sound Thin air meets dense air Light Air meets glass Review In all cases What gets transported by the wave What does the transporting Colton Lecture 25 12 2 08 pg 9 Speed frequency wavelength m s wave s m wave v f Worked Problem AM 1320 broadcasts the Utah Jazz games at a frequency of 1320 kHz Radio waves travel at the speed of light 3 108 m s a What is the wavelength of the AM1320 radio waves b What is the period Colton Lecture 25 12 2 08 pg 10 What will changing the tension do Web demo continued v T For waves on a rope string etc book uses symbol F for tension What happens when you increase the wave speed while keeping the wavelength constant Demo violin Colton Lecture 25 12 2 08 pg 11 Colton Lecture 25 12 2 08 pg 12 Review problems Clicker quiz Two guitar strings of the same length have the same tension but one has four times the mass of the other The speed of a wave on the heavier guitar string is that of the lighter string a b c the same as d 2 e 4 Clicker quiz A boy shakes a rope moving his hand up and down He sends a wave crest out every 0 5 seconds He sees the wave crests move away with a distance between them of 25 cm How fast is the wave moving a 0 10 cm s b 10 20 cm s c 20 30 cm s d 30 40 cm s e more than 40 cm s Colton Lecture 25 12 2 08 pg 13