Class XII Physics: Oscillations Overview

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Questions and Answers

What is the time taken for one complete oscillation or rotation?

  • Amplitude
  • Angular velocity
  • Time period (correct)
  • Frequency

Which of the following is an example of periodic motion but not oscillatory motion?

  • To and fro motion of atoms in a substance
  • Motion of fan blades rotating with constant angular velocity (correct)
  • Swinging a pendulum in a clock
  • The vibration of strings in a guitar

What is the relationship between frequency and time period?

  • Frequency is inversely proportional to time period (correct)
  • Frequency and time period are independent of each other
  • Frequency is directly proportional to time period
  • Frequency is the square of the time period

What is the SI unit of frequency?

<p>Hertz (A)</p> Signup and view all the answers

What is the maximum displacement of a particle from its equilibrium position in simple harmonic motion?

<p>Amplitude (A)</p> Signup and view all the answers

What is the angular displacement of a particle in one complete rotation?

<p>2π (D)</p> Signup and view all the answers

What is the formula for the period of a simple harmonic motion?

<p>T = 2π/ω (D)</p> Signup and view all the answers

What is the displacement equation of simple harmonic motion, where y is the displacement, A is the amplitude, ω is the angular velocity, and t is time?

<p>y = A sin(ωt) (D)</p> Signup and view all the answers

What is the relationship between the spring constant and the total energy of a simple harmonic oscillator?

<p>The spring constant is directly proportional to the total energy. (B)</p> Signup and view all the answers

For a simple harmonic oscillator, at what position is the kinetic energy maximum and the potential energy minimum?

<p>At the mean position (D)</p> Signup and view all the answers

A body of mass 0.1 kg is executing simple harmonic motion according to the equation x = 0.5cos(100t + 3𝜋/4) meters. What is the frequency of oscillation?

<p>50 Hz (D)</p> Signup and view all the answers

In the given SHM equation for a body of mass 0.1 kg, x = 0.5cos(100t + 3𝜋/4) meters, what is the maximum acceleration of the body?

<p>5000 m/s² (C)</p> Signup and view all the answers

A student designs a toy that undergoes simple harmonic motion with amplitude A. At what distance from the mean position does the kinetic energy of the toy become equal to its potential energy?

<p>A/√2 (C)</p> Signup and view all the answers

The following statement is made: "When the potential energy and kinetic energy are equal, the amplitude A of motion of a particle in SHM is ±A/2."

<p>False (B)</p> Signup and view all the answers

A laboratory worksheet recorded timing of 20 oscillations of a spring instead of just one oscillation. This is because the period of oscillation is expected to vary.

<p>False (A)</p> Signup and view all the answers

Which of the following factors affect the period of a simple pendulum?

<p>The length of the pendulum (C), The gravitational acceleration at the location of the pendulum (D)</p> Signup and view all the answers

What is the value of the angle θ when a particle undergoing simple harmonic motion (SHM) reaches its maximum displacement?

<p>90 degrees (D)</p> Signup and view all the answers

What is the relationship between the maximum velocity (v_max) and the angular frequency (ω) of a particle undergoing SHM, given the amplitude (A)?

<p>v_max = ωA (B)</p> Signup and view all the answers

What is the relationship between the maximum acceleration (a_max) and the angular frequency (ω) of a particle undergoing SHM, given the amplitude (A)?

<p>a_max = ω^2A (D)</p> Signup and view all the answers

What is the value of the phase constant (φ) if a particle undergoing SHM has its maximum displacement in the negative x-direction at t = 0?

<p>π (D)</p> Signup and view all the answers

Which of the following statements accurately describes the phase of a particle undergoing SHM?

<p>Phase combines the particle's position and direction of motion at a specific time. (D)</p> Signup and view all the answers

What is the value of the velocity of a particle undergoing SHM at its mean position?

<p>ωA (A)</p> Signup and view all the answers

What is the value of the acceleration of a particle undergoing SHM at its extreme position?

<p>-ω^2A (C)</p> Signup and view all the answers

If the amplitude of a particle undergoing SHM is doubled, what happens to the maximum velocity of the particle?

<p>It doubles. (A)</p> Signup and view all the answers

A body of mass 0.025 kg is attached to a spring with a spring constant of 0.4 N/m. The body is displaced 0.1 m to the right of the mean position and has a velocity of 0.4 m/s. What is the time period of the oscillation?

<p>1.57 s (C)</p> Signup and view all the answers

What is the frequency of the oscillation described in the previous question?

<p>0.63 Hz (C)</p> Signup and view all the answers

What is the angular speed of the oscillation described in the previous questions?

<p>4 rad/s (B)</p> Signup and view all the answers

What is the total energy of the oscillation described in the previous questions?

<p>0.04 J (A)</p> Signup and view all the answers

What is the amplitude of the oscillation described in the previous questions?

<p>0.2 m (B)</p> Signup and view all the answers

What is the maximum velocity of the oscillation described in the previous questions?

<p>0.8 m/s (B)</p> Signup and view all the answers

What is the maximum acceleration of the oscillation described in the previous questions?

<p>1.6 m/s^2 (C)</p> Signup and view all the answers

A simple pendulum is made of a body which a hollow sphere containing mercury is suspended by means of a wire. If a little mercury is drained off, what will happen to the period of the pendulum?

<p>Increase (C)</p> Signup and view all the answers

What is the difference between free oscillation and forced oscillation?

<p>Free oscillation occurs when the body vibrates with its own natural frequency, while forced oscillation occurs when the body vibrates with the help of an external periodic force with a frequency different from the natural frequency. (A)</p> Signup and view all the answers

Which of the following is an example of free oscillation?

<p>A tuning fork vibrating after being struck. (C)</p> Signup and view all the answers

A body oscillates with a time period of 0.5 seconds. What is its frequency?

<p>2 Hz (C)</p> Signup and view all the answers

Which of the following statements is TRUE about simple harmonic motion?

<p>The velocity is maximum at the equilibrium position. (A)</p> Signup and view all the answers

A particle is executing simple harmonic motion with a period of 4 seconds. What is the time taken to complete one-fourth of an oscillation?

<p>1 second (A)</p> Signup and view all the answers

A pendulum is oscillating with a period of 2 seconds. What is the length of the pendulum?

<p>0.99 m (B)</p> Signup and view all the answers

A mass is attached to a spring and is undergoing simple harmonic motion. Which of the following remains constant during the motion?

<p>Total mechanical energy (B)</p> Signup and view all the answers

Which of the following is NOT an example of simple harmonic motion?

<p>A ball rolling down a frictionless inclined plane (A)</p> Signup and view all the answers

Consider a simple pendulum oscillating with a small amplitude. Which of these quantities remains unchanged?

<p>Period (B)</p> Signup and view all the answers

What is the value of the phase angle, ɸ, in radians, for the displacement equation x = 6cosωt + 8sinωt?

<p>0.93 radians (C)</p> Signup and view all the answers

What is the amplitude, D, of the resultant SHM represented by the equation x = 6cosωt + 8sinωt?

<p>10 m (C)</p> Signup and view all the answers

If A and B are the amplitudes of two waves, what is the formula for the resultant amplitude D of the superposition of these waves?

<p>D = √(A² + B²) (D)</p> Signup and view all the answers

What does ω represent in the equation x = 6cosωt + 8sinωt?

<p>Angular frequency (C)</p> Signup and view all the answers

Which variable represents the spring constant in Hooke's law: F = -kx?

<p>k (A)</p> Signup and view all the answers

What is the relationship between potential energy (PE) in a spring and its displacement x?

<p>PE is directly proportional to the square of the displacement (D)</p> Signup and view all the answers

In the equation v = -ωA sinωt, what does v represent?

<p>Velocity (B)</p> Signup and view all the answers

What is the relationship between the time period of the combined periodic functions and the individual time periods of the functions?

<p>The time period of the combination is equal to the minimum time period among the individual functions (C)</p> Signup and view all the answers

Flashcards

Periodic Motion

Motion that repeats after a specific time interval.

Oscillatory Motion

Motion where a body moves back and forth about a fixed point.

Simple Harmonic Motion

Motion where force is proportional to and opposite to displacement.

Equilibrium Position

The position where forces are balanced and the system is at rest.

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Restoring Force

Force that brings a system back to its equilibrium position.

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Time Period

The time taken for one complete cycle of motion.

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Frequency

The number of cycles per unit time, usually in seconds.

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Relation to Circular Motion

Simple harmonic motion is linked to uniform circular motion.

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Simple Harmonic Motion (SHM)

A specific type of oscillatory motion projected from uniform circular motion.

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Time Period (T)

The time taken for one complete cycle of motion.

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Frequency (f)

The number of complete oscillations per second.

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Amplitude (A)

The maximum distance from the mean position in SHM.

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Angular Velocity (ω)

The rate of change of angular displacement, usually in radians per second.

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Displacement Equation of SHM

y = A sin(ωt), describes position at any time in SHM.

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Resultant Displacement

The total displacement from two waves combined, represented as z(t) = D sin(ωt + φ).

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Phase Angle

The angle φ that represents the phase difference in superimposed waves, calculated by φ = tan⁻¹(B/A).

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Resultant Amplitude

The combined amplitude D derived from two wave amplitudes A and B, given by D = √(A² + B²).

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Potential Energy (PE) in SHM

Energy stored in the system, proportional to displacement, expressed as PE = (1/2)kx².

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Kinetic Energy (KE) in SHM

Energy due to motion, expressed in terms of mass and velocity as KE = (1/2)mv².

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Hooke's Law

States that the restoring force exerted by a spring is proportional to the displacement, F = -kx.

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Displacement Function

The expression for the position of a particle over time in SHM, e.g., x(t) = 6cos(ωt) + 8sin(ωt).

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Time Period of SHM

The time taken for one complete cycle of the motion, equal to the minimum period of combined functions.

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Angular Speed (ω)

Rate of change of angular displacement in oscillation.

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Total Energy in SHM

The energy stored in a spring during oscillation, constant over time.

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Amplitude

The maximum displacement from the mean position in an oscillation.

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Maximum Velocity

The highest speed reached by an object in simple harmonic motion.

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Free Oscillation

Oscillation of a system without external force, at its natural frequency.

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Forced Oscillation

Oscillation driven by an external periodic force.

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Car Suspension System

A mechanism balancing stiffness and comfort for vehicle handling.

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Spring Constant

A value matching the stiffness of a spring to weight and conditions.

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Total Energy (TE)

The sum of kinetic energy (KE) and potential energy (PE) in a system.

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Simple Pendulum Energy Equation

TE = PE + KE; KE is max at mean position, PE is max at extremes.

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Amplitude (A) in SHM

Maximum displacement from mean position in simple harmonic motion.

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Frequency of Oscillation

The number of cycles in a given time; affects motion speed.

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Maximum Acceleration

Greatest rate of change of velocity in SHM, linked to amplitude and period.

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Maximum Displacement

The furthest distance a particle moves from its equilibrium position in SHM, occurring at extreme positions.

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Displacement in SHM

Describes the position of a particle from its equilibrium in simple harmonic motion, represented as y = A sin(ωt).

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Velocity in SHM

The speed of a particle in simple harmonic motion, given by v = ωA cos(ωt).

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Acceleration in SHM

Rate of change of velocity, calculated as a = -ω²A sin(ωt) in simple harmonic motion.

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Phase Constant (φ)

A measure determining the initial position and motion direction of a SHM particle at t = 0, influencing the motion equation.

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Maximum Velocity (V max)

The highest speed reached by a particle in SHM, calculated as V max = ωA.

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Maximum Acceleration (a max)

The highest acceleration in SHM, calculated as a max = ω²A, occurring at extreme positions.

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Graphical Representation in SHM

Visual depiction of displacement, velocity, and acceleration over time in simple harmonic motion using sine and cosine curves.

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Study Notes

Summary of Provided Information

  • Welcome! (Page 1)
  • MOMO/DUMPLING PHYSICS (Page 2)
  • Introduction to Class XII Physics - 2024 (Page 3)
  • This document presents detailed information about physics, specifically focusing on the topic of oscillations for a 12th grade class. Various aspects are covered, such as timing, weighting, scope, and fundamental concepts. (Page 3, 5, 6, 7, 8, 9, 10, 11-19, 21-22, 23-30, 31-33, 34-35, 36-37, 38-40, 41-48, 49-56, 57-66, 68-78, 79-82)
  • Topics and weighting for the XII physics course are presented. (Page 5)
  •  Subtopics of periodic and oscillatory motion and simple harmonic motion are presented (pages 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25 , 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 , 36,37, 40, 41, 42, 43, 44, 47-56, 58-62, 63-64, 16, 65). Various concepts and formulas for these topics are given, along with examples and exercises. (Pages 13-19, 21-22, 23-30, 31-33, 34-35, 36-37, 38-40, 41-48, 49-51, 52-53, 54-56, 57-60, 62-66, 68-69, 70-72, 73-78, 79-82).

Detailed Study Notes - Oscillation & SHM

  • Periodic Motion: The motion of an object that repeats itself at regular intervals of time. Examples include a pendulum swinging or the hands on a clock.

  • Oscillatory Motion: A type of periodic motion where a body moves back and forth repeatedly about a fixed point. For example, a pendulum or a simple harmonic oscillator.

  • Simple Harmonic Motion (SHM): A special type of oscillatory motion characterized by a restoring force that is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. The motion repeats itself in a sinusoidal pattern.

  • Amplitude: The maximum displacement from the equilibrium position during an oscillation.

  • Period (T): The time taken for one complete oscillation to occur.

  • Frequency (f): The number of oscillations completed in one second. The relationship is f = 1/T.

  • Angular Frequency (ω): The rate at which the angle changes for an oscillation, given by ω = 2πf.

  • Phase: The current position and direction of the moving object of a SHM at any instant given by wt + ø.

  • Phase Constant (φ): A constant that defines the initial phase of the oscillation relative to the specified direction. 

  • Displacement equation of SHM (cosine): x = A cos(ωt + φ), where A is amplitude, ω is angular frequency, t is time, and φ is the phase constant

  • Displacement equation of SHM (sine): x = A sin(ωt + φ)

  • Velocity in SHM : v = -ωA sin(ωt + φ)

  • Acceleration in SHM: a = -ω²A cos(ωt + φ)

  • Relationship between acceleration and displacement: In SHM, acceleration is directly proportional to the displacement, but opposite in direction. (Equation: a = -ω²x)

  • Energy in SHM: The total energy in SHM is the sum of potential energy (PE) and kinetic energy (KE), with each changing as the other decreases, maintaining a constant total amount. These are respectively given by:

  •  PE = ½ kA2 cos2(ωt + φ) 

  •  KE = ½ mω2A2 sin2(ωt + φ) 

  • Total energy in SHM: Total Energy is constant and is given by TE = ½kA2 = ½mω2A2.

  • Relationship of period with frequency and other factors like Mass m, Spring constant k .

  • Examples of SHM: a swinging pendulum, a mass attached to a spring, the motion of a ball in a bowl.

  • Difference between periodic and oscillatory motions: Periodic motion is any motion that repeats itself in regular intervals. Oscillatory motion is a kind a periodic motion, where the motion is back and forth about a central point.  

  • Concept of Resonance (i) and (ii)

  • Experiment setups and materials Used (i),(ii), and others... (Page 68, 70, 71, 72, 73, 75).

  • Procedure of experiments and observations, (Page 71)

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