Waves and oscillation tebranishlar va to’lqinlar


Pendulum. You all must have seen the pendulum in the clocks moving to and



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physics module 1 notes final (1)

Pendulum. You all must have seen the pendulum in the clocks moving to and fro regularly

  • Swing. Swings in the parks are also the example of simple harmonic motion

  • Car Shock Absorber.

  • Musical Instruments.

    Mayatnik. Siz hammangiz soatlardagi mayatnikni muntazam ravishda u yoqdan-bu yoqqa harakatlanayotganini ko'rgan bo'lsangiz kerak


    Belanchak. Parklardagi belanchaklar ham oddiy garmonik harakatning namunasidir
    Avtomobil amortizatori.
    Musiqiy asboblar.



    • Bungee Jumping.

    • Hearing.




    • Cradle.

    CAR SHOCK ABSORBER SIMPLE PENDULUM MUSICAL INSTRUMENT


    TYPES OF OSCILLATION
    TEBRANISH TURLARI

      • FREE OSCILLATION

      • DAMPED OSCILLATION

      • FORCE OSCILLATION

      • Erkin tebranishlar

      • So’nuvchi tebranishlar

      • Majburiy tebranishlar




      • FREE OSCILLATION:

      • Erkin tebranishlar

    A free oscillation is an ideal condition where a particle's motion is not under the influence of any external resistance. It is a motion with a natural frequency of the particle and constant amplitude, energy, and period.
    Erkin tebranish - zarracha harakati hech qanday tashqi qarshilik ta'sirida bo'lmagan ideal holat. Bu zarrachaning tabiiy chastotasi va doimiy amplitudasi, energiyasi va davri bo'lgan harakatdir.

    Graphical representation of free oscillation


    Erkin tebranishning grafik tasviri

    DAMPED OSCILLATION:


    So’nuvchi tebranishlar:
    The effect of radiation by an oscillating system and of the friction present in the system is that the amplitude of oscillations gradually diminishes with time. The reduction in amplitude (or energy) of an oscillator is called damping and the oscillation are said to be damped.

    Tebranuvchi tizimning nurlanishining va tizimda mavjud bo'lgan ishqalanishning ta'siri shundaki, tebranishlar amplitudasi vaqt o'tishi bilan asta-sekin kamayadi. Osilator amplitudasining (yoki energiyasining) kamayishi damping deb ataladi va tebranish so'ndiriladi.



    Graphical representation of damped oscillation


    Sönuvchi tebranishning grafik tasviri

    FORCED OSCILLATION:


    Majburiy tebranish:
    Forced oscillations occur when an oscillating system is driven by a periodic force that is external to the oscillating system.
    Majburiy tebranishlar tebranish sistemasiga tashqi bo‘lgan davriy kuch ta’sirida harakatlansa sodir bo‘ladi.

    Graphical representation of force oscillation


    Majburiy tebranishlarining grafik tasviri
    DIFFERENTIAL EQUATION
    DIFFERENTSIAL TENGLAMA
    a differential equation is an equation that relates one or more functions and their derivatives.
    differensial tenglama - bu bir yoki bir nechta funksiya va ularning hosilalarini bog'laydigan tenglama.
    Velocity of a body in terms of differential equation is given by
    Jismning differensial tenglama bo'yicha tezligi quyidagicha berilgan
    V = 𝒅𝒙
    𝒅𝒕
    Acceleration of body in terms of differential equation is given by
    Jismning differensial tenglama bo'yicha tezlanishi bilan berilgan


    A = 𝒅𝟐𝒙
    𝒅𝒕𝟐
    DERIVE AN EXPRESSION FOR DIFFERENTIAL EQUATION OF FREE OSCILLATION
    ERKIN TEBRANISHNING DIFFERENTIAL TENGLAMASINI KELTIRIB CHIQARISH.
    Let a body be initiated to an oscillatory motion after being displaced from its equilibrium position and left free
    Jism o'z muvozanat holatidan siljigan va erkin qoldirilgandan so'ng tebranish harakatiga tushsin.
    For such oscillations, the lonely force acting on the body will be the restoring force F
    Bunday tebranishlar uchun jismga ta'sir qiluvchi yolg'iz kuch F tiklovchi kuch
    bo'ladi

    WE KNOW THAT,


    For a vibrating body
    F = -Kx (1)
    Where, x is the displacement and K is the force constant
    Bu erda x - siljish va K - kuch doimiysi
    If ‘m’ is the mass of the body then as per newton’s 2nd law of motion,

    Now by equation (1) and (2)


    𝒅𝟐𝒙
    𝑭 = 𝒎 𝒅𝒕𝟐 … … … … … … (𝟐)

    𝒎 𝒅𝟐𝒙 = -kx (3)


    𝒅𝒕𝟐
    𝒅𝟐𝒙 = 𝒌 𝒙 … … … . . (𝟒)

    𝒅𝒕𝟐 𝒎
    𝒅𝟐𝒙 + 𝒌 𝒙 = 𝟎 … … … . (𝟓)
    𝒅𝒕𝟐 𝒎
    The equation number 5 represents the differential equation of free oscillation (it is also representing the equation of simple harmonic motion)
    5-raqamli tenglama erkin tebranishning differentsial tenglamasini ifodalaydi (bu oddiy garmonik harakat tenglamasini ham ifodalaydi)


    DERIVE AN EXPRESSION FOR DISPLACEMENT OF AN DAMPED OSCILLATION
    The damped system is subjected to


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