Simple Harmonic Motion Basics
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Questions and Answers

What is the physical significance of the term A in the equation of simple harmonic motion?

  • It represents the maximum displacement of the particle (correct)
  • It is the time period of the motion
  • It is the angular frequency of the motion
  • It is the phase constant of the motion

    • What is the physical significance of the term φ in the equation of simple harmonic motion?

  • It is the amplitude of the motion
  • It is the time period of the motion
  • It is the angular frequency of the motion
  • It is the phase constant of the motion (correct)

    • What is the relation between ω and T in simple harmonic motion?

  • ω is inversely proportional to T squared
  • ω is directly proportional to T squared
  • ω is inversely proportional to T (correct)
  • ω is proportional to T

    • What is the physical significance of the term (ωt + φ) in the equation of simple harmonic motion?

    <p>It is the phase of the motion at time t</p> Signup and view all the answers

    What can be said about two simple harmonic motions with the same A and ω but different φ?

    <p>They have different phase angles</p> Signup and view all the answers

    What is the unit of the angular frequency ω in simple harmonic motion?

    <p>radians per second</p> Signup and view all the answers

    What is the significance of taking φ = 0 in the equation of simple harmonic motion?

    <p>It simplifies the equation of motion</p> Signup and view all the answers

    What is the physical significance of the graph shown in Fig. 13.7(b)?

    <p>It shows two simple harmonic motions with the same amplitude and angular frequency but different phase angles</p> Signup and view all the answers

    What is the angular speed of the particle P?

    <p>ω rad/s</p> Signup and view all the answers

    What is the initial angle made by the position vector OP with the positive direction of the x-axis?

    <p>φ</p> Signup and view all the answers

    What is the angle made by the position vector OP with the positive direction of the x-axis at time t?

    <p>ωt + φ</p> Signup and view all the answers

    What is the projection of the position vector OP on the x-axis?

    <p>OP′</p> Signup and view all the answers

    What is the expression for sin(ωt) - cos(ωt) in terms of ωt?

    <p>√2 sin(ωt - π/4)</p> Signup and view all the answers

    What is the sense of rotation of the particle P?

    <p>Anticlockwise</p> Signup and view all the answers

    What is the radius of the circle on which the particle P is moving?

    <p>A</p> Signup and view all the answers

    What is the angle covered by the particle P in time t?

    <p>ωt</p> Signup and view all the answers

    What is the nature of the velocity of a particle executing SHM?

    <p>Periodic function of time</p> Signup and view all the answers

    At what position is the kinetic energy of a particle in SHM zero?

    <p>At the extreme positions of displacement</p> Signup and view all the answers

    What is the relationship between kinetic and potential energies of a particle in SHM?

    <p>They vary between zero and their maximum values</p> Signup and view all the answers

    What is the direction of the displacement of the mass in Fig. 13.15?

    <p>To the right side of the equilibrium position</p> Signup and view all the answers

    What is the definition of kinetic energy (K) of a particle in SHM?

    <p>It is defined as the product of mass and velocity</p> Signup and view all the answers

    What can be said about the kinetic energy and potential energy of a particle in SHM?

    <p>They vary between zero and their maximum values</p> Signup and view all the answers

    What is the angle made by OP with the x-axis at time t = 0?

    <p>45°</p> Signup and view all the answers

    What is the angle covered by the particle P in the anticlockwise sense after time t?

    <p>2πt</p> Signup and view all the answers

    What is the expression for the displacement of the particle P′ on the x-axis?

    <p>x(t) = A cos(ωt + φ)</p> Signup and view all the answers

    What is the period of the SHM given by the equation x(t) = A cos(2πt/4 + π/4)?

    <p>4 s</p> Signup and view all the answers

    What is the phase difference between the projections of the motion of P on the x-axis and the y-axis?

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

    What is the expression for the displacement of the particle P′ on the y-axis?

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

    What is the amplitude of the SHM given by the equation x(t) = A cos(2πt/4 + π/4)?

    <p>A</p> Signup and view all the answers

    What is the force acting on a particle in linear simple harmonic motion?

    <p>A force different from centripetal force</p> Signup and view all the answers

    What is the total mechanical energy of a simple harmonic motion system if no friction is present?

    <p>Constant and remains the same</p> Signup and view all the answers

    What type of force is responsible for simple harmonic motion?

    <p>Hooke's law restoring force</p> Signup and view all the answers

    What is the period of oscillation of a simple pendulum swinging through small angles?

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

    What is the characteristic of a linear oscillator?

    <p>Governed by Hooke's law restoring force</p> Signup and view all the answers

    What is the condition for a periodic motion to be simple harmonic?

    <p>The force must be proportional to the displacement</p> Signup and view all the answers

    What is the relation between the kinetic energy and potential energy of a simple harmonic motion system?

    <p>K + U = E</p> Signup and view all the answers

    What is the condition for circular motion to arise due to a simple harmonic force?

    <p>The phases of motion in two perpendicular directions must differ by π/2</p> Signup and view all the answers

    What is the period of a simple harmonic motion system?

    <p>T = 2π√(m/k)</p> Signup and view all the answers

    Study Notes

    Simple Harmonic Motion (SHM)

    • SHM is a type of periodic motion where the particle moves back and forth about its equilibrium position.
    • The amplitude (A) of SHM is the magnitude of the maximum displacement of the particle.
    • The phase (ωt + φ) of SHM is the quantity that determines the initial position of the particle at t = 0.
    • The phase constant (φ) is the value of the phase at t = 0.

    Angular Frequency (ω)

    • The angular frequency (ω) is related to the period of motion (T) by the equation ω = 2π / T.
    • The angular frequency (ω) is also related to the period of revolution of a particle moving uniformly on a circle.

    Simple Harmonic Motion Equation

    • The equation of SHM is x(t) = A cos (ωt + φ).
    • The equation of SHM can also be written in terms of sine function as x(t) = A sin (ωt + φ + π/2).

    Projection of Circular Motion on a Diameter

    • When a particle moves uniformly on a circle, its projection on a diameter executes SHM.
    • The projection of the motion on the x-axis is given by x(t) = A cos (ωt + φ).
    • The projection of the motion on the y-axis is given by y(t) = A sin (ωt + φ), which is also an SHM with the same amplitude but differing by a phase of π/2.

    Energy in Simple Harmonic Motion

    • The kinetic energy (K) of a particle in SHM varies between zero and its maximum value.
    • The potential energy (U) of a particle in SHM varies between zero and its maximum value.
    • The mechanical energy (E) of a particle in SHM remains constant, E = K + U.

    Period and Frequency of SHM

    • The period (T) of SHM is the time taken by the particle to complete one oscillation.
    • The frequency (f) of SHM is the number of oscillations per second, f = 1 / T.
    • The angular frequency (ω) is related to the period by ω = 2π / T.

    Points to Ponder

    • The period (T) is the least time after which the motion repeats itself.
    • Not every periodic motion is SHM; only that periodic motion governed by the force law F = – k x is SHM.
    • Circular motion can arise due to an inverse-square law force or due to SHM in two dimensions.

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    Description

    Understand the concepts of Simple Harmonic Motion, including amplitude, phase, and phase constant. Learn how to determine the amplitude and phase constant from the displacement at t = 0.

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