Physics 113 01. Oscillations and SHM Prof. Pieter Neethling pietern@sun.ac.za Fisika 113 01. Ossillasies en EHB Mr. Riyaadh Jamodien riy@sun.ac.za Oscillations Ossillasie from the Latin oscillare meaning to swing van die Latyn woord oscillare wat beteken om te swaai Ossillasie Oscillations Oscillation: a movement back and forth in a regular rhythm Ossillasie : 'n beweging heen en weer in 'n gereelde ritme Found everywhere in nature, from the smallest to the largest objects. Molecular systems to skyscrapers and bridges Word oral in die natuur aangetref, van die kleinste tot die grootste voorwerpe: molekulêre stelsels, wolkekrabbers en brûe The bridge collapsed on 7 November 1940, 4 months after opening, because the engineers did not account for the bridge’s oscillation in their design! Die brug het op 7 November 1940, 4 maande na dit oopgestel is, ingeval omdat die ingenieurs nie in ag geneem het dat die brug kon ossilleer! Oscillatory Motion can also be called periodic motion Periodic motion: motion that repeats itself from the Greek: periodos meaning orbit Period: The time it takes to complete one cycle (i.e. oscillation) Frequency: The number of cycles (oscillations) that occur in 1 second Ossillerende beweging word ook periodiese beweging genoem Periodiese beweging: beweging wat homself herhaal van die Griekse word: periodos wat beteken om te wentel Periode: Die tyd wat dit neem om een siklus (m.a.w. ossilasie) te voltooi Frekwensie: Die aantal siklusse (ossilasies) wat in 1 sekonde voltooi word Force that a spring exerts on an object / Krag wat Ε veer op Ε voorwerp uitoefen. Eenvoudige harmoniese beweging (EHB) Simple harmonic motion (SHM) SHM is a type of periodic motion (i.e. motion that repeats itself) EHB is 'n soort periodiese beweging (d.w.s. beweging wat homself herhaal) It occurs in systems which obey the equation: πΉ = −ππ₯ Force Spring constant displacement πΉ = −ππ₯ πΉ is the force that the spring exerts on the mass and is known as a restoring force It tries to restore the object to equilibrium. Dit kom voor in stelsels wat die volgende vergelyking gehoorsaam: πΉ = −ππ₯ Krag Hooke’s Law veerkonstante πΉ = −ππ₯ π₯=0 verplasing Hooke se Wet πΉ is die krag wat die veer op die massa uitoefen en staan bekend as 'n herstellende krag. Dit probeer om die voorwerp in ewewig te herstel. −π₯ +π₯ SHM can be modelled using a sinusoidal function (i.e. a π ππ function or a πππ function) EHB kan gemodelleer word met behulp van 'n sinusvormige funksie (d.w.s. 'n π ππ funksie of Ε πππ funksie) π₯ π‘ = π΄ cos(ππ‘) A mass on a spring exhibits SHM (Simple Harmonic Motion). Therefore, we can model it using the πππ (or πππ) function ’n Massa op ’n veer vertoon EHB (Eenvoudige Harmoniese Beweging). Daarom kan ons dit met behulp van ’n πππ (of πππ) – funksie modelleer ? A ? -A A mass on a spring exhibits SHM (Simple Harmonic Motion). Therefore, we can model it using the πππ (or πππ) function ’n Massa op ’n veer vertoon EHB (Eenvoudige Harmoniese Beweging). Daarom kan ons dit met behulp van ’n πππ (of πππ) – funksie modelleer π₯[π] 4 0 π‘[π ] −4 π₯=0 π₯ π₯ = −4 π₯=4 A mass on a spring exhibits SHM (Simple Harmonic Motion). Therefore, we can model it using the πππ (or πππ) function ’n Massa op ’n veer vertoon EHB (Eenvoudige Harmoniese Beweging). Daarom kan ons dit met behulp van ’n πππ (of πππ) – funksie modelleer π₯[π] 4 0 π‘[π ] −4 Note how horizontal motion is mapped to a vertical axis π₯=0 π₯ = −4 π₯=4 Let op hoe horisontale beweging na ‘n vertikale as geneem is. cos graphs at high school cos grafieke op hoërskool π¦ π₯ = π΄ cos(π₯) π¦ A π₯ -A cos graphs at high school cos grafieke op hoërskool π¦ π₯ = π΄ cos(ππ₯) π¦ A Greek letter omega: π₯ -A π¦ π₯ = π΄ cos(ππ₯) What happens if I make π bigger? / Wat gebeur as ek π groter maak? What happens if I make π smaller? / Wat gebeur as ek π kleiner maak? Simple harmonic motion (SHM) SHM equation of motion / EHB vergelyking van beweging Eenvoudige harmoniese beweging (EHB) π₯ π‘ = π΄ cos(ππ‘) π₯[π] A π‘[π ] -A Eenvoudige harmoniese beweging (EHB) Simple harmonic motion (SHM) SHM Equation π₯ π‘ = π΄ cos(ππ‘) of motion Frequency π΄ is the amplitude of oscillation π΄ is die amplitude van ossillasie π is the angular frequency π is die hoekfrekwensie period 2π π = 2ππ = π 2π π₯ π‘ = π΄ cos π‘ π 2π π₯ π‘ = π΄ cos π‘ π 2π π= π π₯ π‘ = π΄ cos(ππ‘) π₯[π] π π‘[π ] large π small π» π₯[π] π π‘[π ] small π π₯[π] large π» π π‘[π ] Simple harmonic motion (SHM) SHM Equation of motion Eenvoudige harmoniese beweging (EHB) π₯ π‘ = π΄ cos(ππ‘) frequency π΄ is the amplitude of oscillation π΄ is die amplitude van ossillasie π is the angular frequency π is die hoekfrekwensie 2π π₯ π‘ = π΄ cos π‘ π What are the units inside the bracket? Wat is die eenhede binne die hakies? period 2π π = 2ππ = π π¨. π«ππππππ / Grade π©. πΉππ ππππ / Radiale πͺ. π«ππππππππππππ / Dimensieloos π«. πΎπ πππ πππ πππ πππ ππππ / Ons is almal een groot eenheid Oscillatory Motion / Periodic Motion Ossillerende beweging / Periodiese beweging 'n Voorwerp wat aan 'n vertikale veer geheg is, word vrygestel en ossillerende beweging, soos hieronder getoon. Foto's van die beweging word met tussenposes van 1 s geneem. Watter prentjie verteenwoordig die voltooiing van een ossillasie? An object attached to a vertical spring is released and undergoes oscillatory motion as shown below. Pictures of the motion are taken at 1 s intervals. Which picture represents the completion of one oscillation? 0π 1π π£ A B C D E Ossi-wat?! Oscillatory Motion / Periodic Motion An object attached to a vertical spring is released an undergoes oscillatory motion as shown below. Pictures of the motion are taken at 1 s intervals and are shown below. What is the period of this motion? 0π Ossillerende beweging / Periodiese beweging 'n Voorwerp wat aan 'n vertikale veer geheg is, word vrygestel en ondergaan ossillerende beweging, soos hieronder getoon. Fotos van die beweging word met tussenposes van 1 s geneem en word hieronder getoon. Wat is die periode van hierdie beweging? 1π π¨. π, π π π©. π, π π πͺ. π, π π π£ π«. π, π π E Ossi-what?! Oscillatory Motion / Periodic Motion An object attached to a vertical spring is released an undergoes oscillatory motion as shown below. Pictures of the motion are taken at 1 s intervals and are shown below. What is the period of this motion? 0π Ossillerende beweging / Periodiese beweging 'n Voorwerp wat aan 'n vertikale veer geheg is, word vrygestel en ondergaan ossillerende beweging, soos hieronder getoon. Fotos van die beweging word met tussenposes van 1 s geneem en word hieronder getoon. Wat is die periode van hierdie beweging? 1π π¨. π, π π π©. π, π π πͺ. π, π π π£ π«. π, π π E Ossi-what?! Oscillatory Motion / Periodic Motion An object attached to a vertical spring is released an undergoes oscillatory motion as shown below. Pictures of the motions are taken at 1 s intervals and are shown below. What is the frequency of this motion? 0π Ossillerende beweging / Periodiese beweging ‘n Voorwerp wat aan 'n vertikale veer geheg is, word vrygestel en ondergaan ossillerende beweging, soos hieronder getoon. Prente van die bewegings word met tussenposes van 1 s geneem en word hieronder getoon. Wat is die frekwensie van hierdie beweging? 1π π¨. π, ππ π―π π©. π, π π―π πͺ. π, π π―π π£ π«. π, π π―π E Frekwe-huh?! Oscillatory Motion / Periodic Motion An object attached to a vertical spring is released an undergoes oscillatory motion as shown below. Pictures of the motions are taken at 1 s intervals and are shown below. What is the frequency of this motion? 0π Ossillerende beweging / Periodiese beweging ‘n Voorwerp wat aan 'n vertikale veer geheg is, word vrygestel en ondergaan ossillerende beweging, soos hieronder getoon. Prente van die bewegings word met tussenposes van 1 s geneem en word hieronder getoon. Wat is die frekwensie van hierdie beweging? 1π π¨. π, ππ π―π π©. π, π π―π πͺ. π, π π―π π£ π«. π, π π―π E Frequi-huh?! Oscillatory Motion / Periodic Motion Ossillerende beweging / Periodiese beweging A pendulum is pulled to the right hand side and released. At which point will it complete 1 ππ ππππππ‘πππ π. π. 1 ππ¦πππ ? 'n Slinger na regs getrek en vrygelaat. A B D I’m lost/ Verlore!! C Op watter punt sal dit 1 ππ π ππππ ππ (πππ€ 1 π ππππ’π ) voltooi? Oscillatory Motion / Periodic Motion Ossillerende beweging / Periodiese beweging A pendulum is pulled to the right hand side and released. At which point will it complete 1 ππ ππππππ‘πππ π. π. 1 ππ¦πππ ? 'n Slinger na regs getrek en vrygelaat. A D I’m lost B C Op watter punt sal dit 1 ππ π ππππ ππ (πππ€ 1 π ππππ’π ) voltooi?
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