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

    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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    Introduction to Class XII Physics - 2024 PDF

    Description

    This quiz covers essential topics in Class XII Physics focused on oscillations, including periodic motion and simple harmonic motion. It provides a comprehensive review of concepts, formulas, and relevant examples to aid in understanding. Perfect for students preparing for their 12th-grade physics assessments.

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