Simple Harmonic Motion Quiz
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Questions and Answers

What is the maximum displacement of the particle in SHM?

  • 2 cm
  • 1 cm
  • 4 cm (correct)
  • 3 cm

    • What is the acceleration of the particle when it is at a distance of 1 cm from its mean position?

  • 1 cm/s^2
  • 2 cm/s^2
  • 4 cm/s^2
  • 3 cm/s^2 (correct)

    • What is the velocity of the particle when it is at a distance of 2 cm from the mean position?

  • 1 cm/s
  • 3 cm/s
  • 2 cm/s (correct)
  • 4 cm/s

    • Which of the following relationships is correct between the acceleration ‘𝛽′ and the displacement ‘y’ of a particle involved in simple harmonic motion?

    <p>β = -5 𝑦 (A)</p> Signup and view all the answers

    In the simple harmonic motion described by the equation x = 0.25 cos(π/8 t), what is the amplitude of the motion?

    <p>0.25 m (C)</p> Signup and view all the answers

    What is the angular frequency of the simple harmonic motion described by the equation x = 0.25 cos(π/8 t)?

    <p>π/8 rad/s (C)</p> Signup and view all the answers

    What is the period of the simple harmonic motion described by the equation x = 0.25 cos(π/8 t)?

    <p>16 s (D)</p> Signup and view all the answers

    What is the displacement of the object after 2.0 seconds in the simple harmonic motion described by x = 0.25 cos(π/8 t)?

    <p>0.125 m (B)</p> Signup and view all the answers

    What is the period of the oscillation of a 326-g object attached to a spring with a total energy of 5.83 J?

    <p>0.250 s (A)</p> Signup and view all the answers

    What happens to the period of a pendulum when mercury is drained from a hollow sphere?

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

    What defines free oscillation?

    <p>Oscillation without external interference (A)</p> Signup and view all the answers

    What is the correct unit for angular frequency (ω)?

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

    If a block weighing 4 kg stretches a spring by 0.16 m, what will be the effect on the spring's constant when a 0.5 kg block is hung?

    <p>It remains the same (D)</p> Signup and view all the answers

    Which of the following is a characteristic of forced or driven oscillation?

    <p>Requires external energy input (C)</p> Signup and view all the answers

    What is the total energy of a system undergoing simple harmonic motion if the maximum speed is calculated to be 1 m/s?

    <p>5.83 J (A)</p> Signup and view all the answers

    What is true about the maximum acceleration of an object in simple harmonic motion?

    <p>It is dependent on the spring constant and mass (B)</p> Signup and view all the answers

    What does a greater spring constant indicate about a spring?

    <p>It resists compression more effectively. (A)</p> Signup and view all the answers

    How does a stiffer spring affect car stability during cornering?

    <p>Reduces weight transfer. (C)</p> Signup and view all the answers

    Which equation provides the relationship between the spring constant and mass in harmonic motion?

    <p>k = mω^2 (D)</p> Signup and view all the answers

    What is the effect of a softer suspension system on car performance?

    <p>Increases the risk of reduced stability. (D)</p> Signup and view all the answers

    What happens to the car's position when a stiffer spring is used?

    <p>The car is displaced higher from the ground. (D)</p> Signup and view all the answers

    In the context of Hooke's law, what does a higher spring constant imply?

    <p>Higher restoring force at displacement. (B)</p> Signup and view all the answers

    What is the relationship between mass (m) and angular frequency (ω) in terms of spring constant?

    <p>k = mω^2 (D)</p> Signup and view all the answers

    How does stiffer suspension potentially affect driving comfort?

    <p>Decreases comfort by making the ride harsher. (A)</p> Signup and view all the answers

    What primarily determines the natural frequency of an object?

    <p>Various factors including size, shape, and material properties (C)</p> Signup and view all the answers

    Why is it important for aircraft designers to consider natural frequency in wing design?

    <p>To prevent violent flapping that can be dangerous (A)</p> Signup and view all the answers

    What phenomenon occurs when an external driving force's frequency is close to an object's natural frequency?

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

    What happens to a swing's time period if a person standing in the swing sits down?

    <p>The time period decreases (B)</p> Signup and view all the answers

    Which concept best explains the movement of tectonic plates?

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

    How does a change in altitude affect the time period of a pendulum?

    <p>It has no effect regardless of height (B)</p> Signup and view all the answers

    If a guitar string is tensioned, how is its natural frequency affected?

    <p>Increases with higher tension (A)</p> Signup and view all the answers

    What is the effect of damping on the oscillation of a system?

    <p>It decreases the amplitude of oscillation over time (B)</p> Signup and view all the answers

    What happens to the time period of a swing when Miss Dema stands up? Why?

    <p>It increases because the center of mass rises. (C)</p> Signup and view all the answers

    If Miss Dema swings at a higher altitude, what effect does it have on the time period?

    <p>It increases due to a decrease in gravitational force. (C)</p> Signup and view all the answers

    What effect does having Miss Dema's friend on the swing have on the time period?

    <p>The time period increases due to added mass. (A)</p> Signup and view all the answers

    What is the correct equation for the time period of a simple pendulum?

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

    What happens to the time period of a pendulum when it is taken to the Moon?

    <p>It increases due to decreased gravitational force. (D)</p> Signup and view all the answers

    How is the spring constant calculated from the force applied and displacement?

    <p>k = F/x where k is spring constant, F is force, x is displacement. (A)</p> Signup and view all the answers

    What is the relationship between potential energy and position in simple harmonic motion?

    <p>Potential energy varies quadratically with position. (D)</p> Signup and view all the answers

    In the equation T = 2π√(m/k), what does 'm' represent?

    <p>Mass of the body in motion. (B)</p> Signup and view all the answers

    Which of the following accurately distinguishes between periodic and oscillatory motion?

    <p>Oscillatory motion is always periodic, but periodic motion may or may not be oscillatory. (C)</p> Signup and view all the answers

    Which of the following is NOT a characteristic of oscillatory motion?

    <p>Amplitude of oscillation always remains constant over time. (A)</p> Signup and view all the answers

    Which of the following examples represents simple harmonic motion?

    <p>The motion of a pendulum bob. (D)</p> Signup and view all the answers

    A bird flapping its wings circles around a clock tower. What type of motion is the flapping of its wings?

    <p>Periodic but not oscillatory (C)</p> Signup and view all the answers

    In the following examples, which represent periodic motion but NOT simple harmonic motion? (Select all that apply)

    <p>The rotation of the Earth about its axis. (A), Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lowest point. (C), A freely suspended bar magnet displaced from its N-S direction and released. (D)</p> Signup and view all the answers

    What is the key difference between simple harmonic motion and other types of periodic motion?

    <p>Simple harmonic motion involves a restoring force proportional to the displacement and opposite in direction. (D)</p> Signup and view all the answers

    Which of the following is an example of a system that exhibits simple harmonic motion?

    <p>A swinging pendulum (C)</p> Signup and view all the answers

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

    <p>The restoring force is always directed towards the equilibrium position. (D)</p> Signup and view all the answers

    Study Notes

    Summary of Oscillatory Motion

    • Periodic Motion: A motion that repeats after a specific time interval.
    • Oscillatory Motion: A motion in which a body repeatedly moves back and forth about a fixed point.
    • Oscillatory Motion is always periodic but Periodic motion is not always oscillatory
    • Examples of Periodic Motion: pendulum bob, ball rolling back and forth in a round bowl, motion of clock hands
    • Examples of Oscillatory Motion: swinging pendulum, to and fro motion of atoms in a substance, vibrations of strings in a guitar.
    • Examples of Periodic Motion but not Oscillatory Motion: Uniform circular motion, motion of planets.

    Simple Harmonic Motion (SHM)

    • Definition: SHM is a type of oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position and is directed towards the equilibrium position.
    • Characteristics of SHM:
      • Restoring force is proportional to displacement.
      • Restoring force is opposite in direction to displacement.
      • The energy remains conserved.

    Displacement Equation of SHM

    • Equation: x = A sin(ωt + φ) or x = A cos(ωt + φ), where:
      • x is the displacement from the equilibrium position at time t.
      • A is the amplitude (maximum displacement).
      • ω is the angular frequency (rad/s).
      • t is the time.
      • φ is phase constant (initial phase).

    Velocity in SHM

    • Equation: v = ±ω√(A² - x²)
    • This shows velocity is maximum at equilibrium position.

    Acceleration in SHM

    • Equation: a = -ω²x
    • Acceleration is directly proportional to the negative of the displacement from the mean position. Maximum at extreme position.

    Time Period and Frequency

    • Time period (T): The time taken for one complete oscillation.
    • Frequency (f): The number of oscillations per unit time. f = 1/T
    • Angular frequency (ω): ω = 2πf = 2π/T

    Energy in SHM

    • Potential Energy (PE): PE = ½ kx²
    • Kinetic Energy (KE): KE = ½ mv²
    • Total Energy (TE): TE = PE + KE = ½kA²
    • At the extreme positions: PE is maximum, KE is zero, and TE is constant.
    • At the equilibrium position: PE is zero, KE is maximum, and TE is constant.

    Phase

    • Phase Constant (φ): Initial phase of the motion.
    • Phase: wt + φ, expresses the position and direction of motion

    Resonance

    • Resonance: The phenomenon of increased amplitude of oscillation when the driving force frequency is close to the natural frequency of the oscillator.
    • Aircraft and Resonance: Aircraft designers avoid resonance to stop violent wing flapping caused by forced oscillations.

    Period of a Simple Pendulum

    • Formula: T = 2π√(L/g), where:
      • T is the period.
      • L is the length of the pendulum.
      • g is the acceleration due to gravity.

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    Introduction to Class XII Physics - 2024 PDF

    Description

    Test your understanding of simple harmonic motion (SHM) with this quiz. It covers concepts such as displacement, acceleration, velocity, amplitude, angular frequency, and period. Challenge yourself with questions based on mathematical equations and relationships in SHM.

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