Oscillations 01 Class Notes NEET 2025 PDF

# YAKEEN 2.0 FOR NEET 2025 ## Lecture-01 - Physics: Oscillations By- Dr. Manish Raj (MR SIR) - $U_{rms} = \sqrt{\frac{3RT}{M}}$ - $U_{max} = \sqrt{\frac{2RT}{M}}$ - $V_{mp} = \sqrt{\frac{8RT}{\pi M}}$ ## Topics to be covered 1. Feel of Simple harmonic motion 2. S.H.M is not a new chapter 3. S...

# YAKEEN 2.0 FOR NEET 2025 ## Lecture-01 - Physics: Oscillations By- Dr. Manish Raj (MR SIR) - $U_{rms} = \sqrt{\frac{3RT}{M}}$ - $U_{max} = \sqrt{\frac{2RT}{M}}$ - $V_{mp} = \sqrt{\frac{8RT}{\pi M}}$ ## Topics to be covered 1. Feel of Simple harmonic motion 2. S.H.M is not a new chapter 3. S.H.M is a good question of Kinematics # Periodic Motion - A motion repeat in the same path after a fixed interval of time (T). ## Examples of Periodic Motion - uniform circular motion - Physical class: 8:45 AM - Rotation of earth - Satellite motion - Simple Pendulum ## Periodic motion but no to and fro motion - Motion is periodic - There is no mean position ## Amplitude is too large, so it is not S.H.M - Large amplitude - Not S.H.M. ## Small Amplitude S.H.M - Small amplitude - S.H.M - Energy conserved ## Bouncing of ball between two walls (elastic) - Bouncing of ball between two walls - Elastic motion ### Definition of Periodic motion - Periodic motion repeats itself after an equal interval of time - The interval of time is called time period (T) ### Definition of Oscillation - Oscillation is a periodic motion for a bounded body around a mean point. - Vibration is a high frequency oscillation # **+** PERIODIC MOTION - ***Periodic Motion***: Motion which **repeats itself** after an **equal intervals of time**. The interval of time is called **periodic motion** and **period of periodic motion**. - ***Oscillation***: Oscillation or vibration motion is refined as a **periodic and bonded motion** of a body about a **fixed point**. - Vibration → **High frequency** # **+** PERIOD AND FREQUENCY - Period (T) is the smallest interval of time after which the motion is repeated. - Frequency (v) is the number of oscillations per unit time. - Frequency (v) is the reciprocal of time period (T). - $v = \frac{1}{T}$ - $f = \frac {1}{T} Hz$ - Angular frequency (ω) = $\frac{2π}{T}$ = $2πf$ - Unit of angular frequency is rad/sec # **+** CONDITION OF SHM - S.H.M is a non-uniform motion with a non-uniform arc. - ***Energy is conserved*** - ***Amplitude doesn’t change*** - ***Displacement is around stable equilibrium*** - ***Restoring Force is always directed toward mean position*** - ***Acceleration is always directed towards the mean position*** # **+** SIMPLE HARMONIC MOTION - $a c \propto -x$ (Position) - a ∝ -x (less amplitude, energy conserved, stable equilibrium) - $a \propto (\frac{x}{m})^{n}$. - If n=1, 3, 5, 7… then the motion is oscillatory. - If n = 2, 4, 6, 8… then the motion is translational. # **+** SIMPLE HARMONIC MOTION - The motion of a particle is SHM if the acceleration of a particle is proportional to the displacement from the mean position. - Motion is SHM only when $a \propto -x$ # **+** SIMPLE HARMONIC MOTION - $x = A sin(ωt + φ)$ (general equation) - φ is the initial phase - At t=0, x=0 (start from mean), then φ = 0. - At t=0, x=A (start from extreme), then φ = ½π. # **+** SIMPLE HARMONIC MOTION - Displacement ∝ sin(ωt + φ) - Velocity ∝ cos(ωt + φ) - Acceleration ∝ -sin(ωt + φ) - Velocity is ahead of displacement by phase angle of π/2. - Acceleration is ahead of velocity by phase angle of π/2. - Acceleration is ahead of displacement by phase angle of π. # **+** SIMPLE HARMONIC MOTION - If motion starts from mean position, then the equation of displacement, velocity and acceleration are: - $x = A sin(ωt)$ - $v = Aω cos(ωt)$ - $a = -Aω^2 sin(ωt)$ - If motion starts from extreme position, then the equation of displacement, velocity and acceleration are: - $x = A cos(ωt)$ - $v = -Aω sin(ωt)$ - $a = -Aω^2 cos(ωt)$ # **+** SIMPLE HARMONIC MOTION - Velocity of particle is maximum at the mean position. - Velocity of particle is minimum at the extreme position. - Acceleration of particle is also maximum at the extreme position because displacement is maximum. - Acceleration of particle is minimum at the mean position because displacement is minimum. ## A particle moved such that a = -4x. Find time period (T)? - $a=-w^2x$ - $w^2 = 4$ - $w = 2$ - $T = \frac{2π}{w} = π$ sec - Time period = π sec # **+** SIMPLE HARMONIC MOTION - In SHM, there is a sinusoidal variation in displacement, velocity and acceleration with respect to time. - At t=0, x=0 (displacement is minimum). - At t=0, v=Aω (velocity is maximum). - At t=0, a=0 (acceleration is minimum). - At t=T/4, x=A (displacement is maximum). - At t=T/4, v=0 (velocity is minimum). - At t=T/4, a=-Aω^2 (acceleration is maximum). - At t=T/2, x=0 (displacement is minimum). - At t=T/2, v=-Aω (velocity is maximum). - At t=T/2, a=0 (acceleration is minimum). - At t=3T/4, x=-A (displacement is maximum). - At t=3T/4, v=0 (velocity is minimum). - At t=3T/4, a=Aω^2 (acceleration is maximum). - At t=T, x=0 (displacement is minimum). - At t=T, v=Aω (velocity is maximum). - At t=T,a=0 (acceleration is minimum). # **+** SIMPLE HARMONIC MOTION - ***Displacement, velocity and acceleration show harmonic variation with time having the same period***. - ***The velocity amplitude, Aω, is ω times the displacement amplitude, A*** - ***The acceleration amplitude, Aω², is ω² times the displacement amplitude, A*** - ***In S.H.M. velocity is ahead of displacement by phase angle of π/2*** - ***In S.H.M. acceleration is ahead of velocity by phase angle of π/2*** - ***In S.H.M. acceleration is ahead of displacement by phase angle of π*** ## A body with a mass of 0.01kg is experiencing SHM at x=0. Find the time period. - Force is given as: F= -80N. - Displacement is given as: x = 0.2m. - Mass is given as: m = 0.01kg. - Find the time period. - The formula is: T = 2 π √m/k. - The force constant, k = F/x = 80N/0.2m = 400 N / m. - Substitute these values into the formula: T = 2π√(0.01kg/400N/m) = 0.01π seconds. # **+** SIMPLE HARMONIC MOTION - The force acting on the particle is given by: F = -kx - where k is the force constant and x is the displacement of the particle from its mean position. - The simple harmonic motion is a motion that repeats itself after an equal interval of time. It is a periodic motion that follows the sinusoidal waveform. It’s a characteristic of a particle whose displacement is proportional to the restoring force acting on the particle. - In essence, the greater the displacement, the greater the restoring force, with the restoring force always acting against the displacement. - The SHM is often described using a sinusoidal function, which creates the smooth and rhythmic motion. - It is represented as: x= A sin(ωt + φ), where: - A is the amplitude of the motion - ω is the angular frequency - φ is the phase angle # **+** SIMPLE HARMONIC MOTION - $x = A sin(wT)$ when motion starts from mean - $x = A cos(wT)$ when motion starts from extreme. # **+** SIMPLE HARMONIC MOTION - $x = A sin(wt+φ)$ - $v = Aω cos(wt+φ)$ - $a = -Aω^2 sin(wt+φ))$ # **+** SIMPLE HARMONIC MOTION - $x = A sin(wt)$, displacement is maximum at t=T/4 and 3T/4 - $x = A sin(wt)$, displacement is minimum at t= 0, T/2, T. - $v= Aω cos(wt)$ and $a = -Aω^2 sin(wt)$, velocity is maximum at t=0, T/2, T. - $v= Aω cos(wt)$ and $a = -Aω^2 sin(wt)$, velocity is minimum at t= T/4 and 3T/4 # **+** SIMPLE HARMONIC MOTION - When the particle is moving from the mean position to the extreme position, its velocity decreases, this is due to the restoring force acting against the particle’s motion. - The restoring force is always pointing towards the mean position and opposes the displacement from the mean position. At the extreme position, the restoring force is maximum, and so the velocity of the particle becomes zero. As the particle starts to accelerate back towards the mean position. The direction of the restoring force then reverses and starts to accelerate the particle in the opposite direction. # **+** SIMPLE HARMONIC MOTION - Some important things should be noted: - Displacement, velocity and acceleration show harmonic variation with time having the same period. - velocity amplitude is ω times the displacement amplitude. - The acceleration amplitude is ω² times the displacement amplitude. - In S.H.M. velocity is ahead of displacement by phase angle of π/2. - In S.H.M. acceleration is ahead of velocity by phase angle of π/2. - In S.H.M. acceleration is ahead of displacement by phase angle of π.