Physics Chapter on Pendulums and SHM
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Questions and Answers

If Miss Dema stands up while swinging, what happens to the period of the swing?

  • The period becomes unpredictable.
  • The period decreases. (correct)
  • The period stays the same.
  • The period increases.

    • What happens to the period of the swing if Dema swings at a higher altitude?

  • The period stays the same. (correct)
  • The period increases.
  • The period decreases.
  • The period becomes unpredictable.

    • If Dema's friend joins her on the swing, what happens to the period?

  • The period decreases.
  • It depends on the friend's mass.
  • The period increases. (correct)
  • The period stays the same.

    • What is the formula for the time period (T) of a simple pendulum?

    <p>$T = 2\pi\sqrt{\frac{l}{g}}$ (D)</p> Signup and view all the answers

    What is the relationship between the time period of a simple pendulum and the acceleration due to gravity?

    <p>They are inversely proportional. (C)</p> Signup and view all the answers

    According to Hooke's law, what is the relationship between the force (F) exerted by a spring and the displacement (x) from its equilibrium position?

    <p>F is directly proportional to x. (C)</p> Signup and view all the answers

    What would happen to the time period of a simple pendulum if the mass of the bob were doubled?

    <p>The period would remain the same. (B)</p> Signup and view all the answers

    Calculate the spring constant (k) of a spring if a force of 0.4 N is required to stretch it by 0.1 m.

    <p>4 N/m (A)</p> Signup and view all the answers

    What is the amplitude of the resultant SHM described by the displacement equation: x = 6cos𝜔t + 8sin𝜔t in meters?

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

    What is the phase angle (in radians) of the resultant SHM described by the displacement equation: x = 6cos𝜔t + 8sin𝜔t?

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

    What is the equation for the resultant displacement z(t) of two waves, x(t) and y(t), given by x(t) = A sin t and y(t) = B cos t?

    <p>z(t) = D sin(t +  ) (B)</p> Signup and view all the answers

    What is the formula for calculating the resultant amplitude D of the combined waves x(t) and y(t)?

    <p>D = √(A^2 + B^2) (C)</p> Signup and view all the answers

    What is the relationship between the restoring force F and the displacement x in a simple harmonic oscillator, according to Hooke's Law?

    <p>F = -kx (A)</p> Signup and view all the answers

    What is the formula for potential energy (PE) in a simple harmonic oscillator, expressed in terms of the spring constant k and displacement x?

    <p>PE = 1/2kx^2 (A)</p> Signup and view all the answers

    Given the velocity of a simple harmonic oscillator is v = -ωA sin ωt, what is the formula for the kinetic energy (KE) of the oscillator?

    <p>KE = 1/2m(ωA sin ωt)^2 (B)</p> Signup and view all the answers

    What is the time period of a combination of periodic functions?

    <p>The minimum time period among the combined functions (D)</p> Signup and view all the answers

    What is the time period (T) of a motion that completes one full oscillation?

    <p>The time taken for one complete oscillation (C)</p> Signup and view all the answers

    Which of the following best describes the frequency (f) of a periodic motion?

    <p>The number of oscillations completed in one second (C)</p> Signup and view all the answers

    What is the unit of frequency in the context of periodic motion?

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

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

    <p>Uniform circular motion (B)</p> Signup and view all the answers

    In simple harmonic motion (SHM), how is the displacement of a particle represented?

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

    What is the amplitude (A) in the context of SHM?

    <p>The maximum displacement from the mean position (D)</p> Signup and view all the answers

    If a pendulum has a frequency of 2 Hertz, what is its period (T)?

    <p>0.5 seconds (D)</p> Signup and view all the answers

    In the formula $ heta = 2 heta_{max}$ for angular displacement, what does $ heta_{max}$ represent?

    <p>The maximum angular displacement (D)</p> Signup and view all the answers

    What is the maximum displacement of a particle in SHM when it reaches extreme position A?

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

    What is the formula for maximum velocity in SHM?

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

    What is the equation for acceleration in SHM?

    <p>a = -ω^2 A sin ωt (A)</p> Signup and view all the answers

    What is the maximum acceleration at an extreme position if the amplitude is 10 cm and maximum speed is 5 m/s?

    <p>250 m/s² (D)</p> Signup and view all the answers

    If a particle is at maximum displacement in the positive x-direction, what is the phase φ?

    <p>0 (A)</p> Signup and view all the answers

    As the particle crosses its equilibrium position at maximum velocity, which phase constant φ applies?

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

    What is the formula representation of displacement in SHM at any time t?

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

    What describes the direction of motion and position of a particle in SHM at a given time?

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

    What is the expression that represents the acceleration of a particle in simple harmonic motion related to its displacement?

    <p>β = -ω²y (C)</p> Signup and view all the answers

    If the displacement of a particle in SHM is given by y = 0.2 sin(50πt + 1.57), which of the following represents the amplitude of this motion?

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

    A particle in SHM has a maximum displacement of 4 cm. If its acceleration is 3 cm/s² at a distance of 1 cm from the mean position, what will be its velocity at 2 cm from the mean position?

    <p>6 cm/s (B)</p> Signup and view all the answers

    For the SHM equation x = 0.25 cos(π/8 t), what is the angular frequency?

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

    In the equation V = ωA√(1 - (x²/A²)), which variable represents the displacement from the mean position?

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

    What is the maximum acceleration of a particle in SHM if its maximum speed is known to be 10 cm/s and its amplitude is 5 cm?

    <p>50 cm/s² (A)</p> Signup and view all the answers

    Which relationship between acceleration (β) and displacement (y) is incorrect for a particle undergoing simple harmonic motion?

    <p>β = 3y (D)</p> Signup and view all the answers

    What will be the period of oscillation for a spring-mass system given its angular frequency ω = 4 rad/s?

    <p>π/4 s (D)</p> Signup and view all the answers

    What happens to the period of a simple pendulum if a little mercury is drained off?

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

    What type of oscillation occurs when a body vibrates with its own natural frequency?

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

    If the total energy of a system executing simple harmonic motion is 5.83 J, what does this imply about the maximum speed of the object?

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

    For a block weighing 4 kg that extends a spring by 0.16 m, what will happen if a lighter body is hung from the same spring?

    <p>The period of vibration will increase. (C)</p> Signup and view all the answers

    Which angular frequency is defined as the frequency at which a body oscillates if suddenly disturbed?

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

    What is an example of forced or driven oscillation?

    <p>A person pushing a child on a swing (B)</p> Signup and view all the answers

    What is the relationship between amplitude and total energy in a simple harmonic oscillator?

    <p>Total energy is directly proportional to the square of the amplitude. (A)</p> Signup and view all the answers

    What would be the effect of a second force with a frequency different from the natural frequency on a body?

    <p>It will cause forced oscillation in the body. (C)</p> Signup and view all the answers

    Study Notes

    Summary of Oscillatory Motion

    • Oscillatory motion is a motion in which a body moves back and forth repeatedly about a fixed point in a definite time interval.
    • Periodic motion is any motion that repeats itself at regular intervals; it can be oscillatory but not necessarily so.
    • Oscillatory motion is always periodic.

    Characteristics of Oscillatory Motion

    • Tendency to return to equilibrium or mean position after disturbance.
    • Restoring force is always proportional and opposite to displacement.
    • Energy is conserved in this motion.

    Simple Harmonic Motion (SHM)

    • SHM is a special type of oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position and directed towards it.
    • SHM can be represented as the projection of uniform circular motion onto a diameter of the circle.
    • Displacement equation: x = A sin(ωt + φ) or x = A cos(ωt + φ)
      • A = amplitude
      • ω = angular frequency
      • t = time
      • φ = phase constant

    Time Period and Frequency

    • Time period (T): the time taken for one complete oscillation.
    • Frequency (f): the number of oscillations completed in one second.
      • f = 1/T

    Energy in SHM

    • Total energy (TE) is the sum of potential energy (PE) and kinetic energy (KE).
    • At mean position, KE is maximum and PE is minimum.
    • At extreme position, PE is maximum and KE is zero.
    • Total energy remains constant throughout the motion.

    Factors affecting Time Period

    • Length of the pendulum: Time period is directly proportional to the square root of the length.
    • Acceleration due to gravity: Time period is inversely proportional to the square root of the acceleration due to gravity.
    • Mass of the oscillating object: Time period is independent of the mass of the object.

    Resonance

    • Resonance is a phenomenon in which the amplitude of oscillation increases when the frequency of the driving force is close to the natural frequency of the oscillator.
    • For maximum amplitude displacement:
      • ω = ω₀ (natural frequency)
      • damping constant (b) should be minimum.

    Examples of Oscillatory Motion

    • Pendulum
    • Spring-mass system
    • Swinging
    • Motion of a simple pendulum
    • Motion of an oscillating mercury column in a U-tube
    • Motion of a ball bearing inside a smooth curved bowl
    • Motion of hands of a clock
    • The oscillation of a swing in a park
    • The vibration of strings in a guitar

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    Description

    This quiz covers fundamental concepts related to simple pendulums and simple harmonic motion (SHM). It explores the effects of various factors on the period of a swing, the relationship described by Hooke's law, and calculations involving spring constants. Test your understanding of these important physics concepts through a series of questions.

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