Waves and oscillation tebranishlar va to’lqinlar

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 =} 𝒅^𝟐𝒙
𝒅𝒕^𝟐
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 2^nd law of motion,

Now by equation (1) and (2)

𝒅^𝟐𝒙
𝑭 = 𝒎 _𝒅𝒕𝟐 … … … … … … (𝟐)

𝒎 ^𝒅𝟐^𝒙 = -kx (3)

𝒅𝒕^𝟐
𝒅𝟐^𝒙 = − ^𝒌 𝒙 … … … . . (𝟒)

𝒅𝒕^𝟐 𝒎
^𝒅𝟐^𝒙 + ^𝒌 𝒙 = 𝟎 … … … . (𝟓)
𝒅𝒕^𝟐 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

1.