Simple Harmonic Motion Concepts
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Questions and Answers

What is the value of the spring constant 𝑘 for the spring in the scenario?

  • 0.20 [N/m]
  • 1.00 [N/m]
  • 9.81 [N/m]
  • 3.14 [N/m] (correct)

    • What is the period of oscillation 𝑇 for the weight after being released?

  • 2.00 [s]
  • 4.00 [s]
  • 0.50 [s]
  • 1.00 [s] (correct)

    • What is the angular velocity 𝜔 calculated for this oscillation?

  • 6.28 [rad/s] (correct)
  • 1.57 [rad/s]
  • 12.56 [rad/s]
  • 3.14 [rad/s]

    • What is the amplitude of the oscillation 𝐴 for this system?

    <p>0.20 [m]</p> Signup and view all the answers

    What is the displacement at time 𝑡 = 100 [s] calculated using the given function?

    <p>0.190 [m]</p> Signup and view all the answers

    What is the theoretical maximum speed of the weight as it passes through the equilibrium position O?

    <p>0.39 [m/s]</p> Signup and view all the answers

    Which equation correctly expresses the displacement from the equilibrium position O as a function of time 𝑦(𝑡)?

    <p>𝑦(𝑡) = 0.200 cos(6.28𝑡)</p> Signup and view all the answers

    What does the negative sign in the force equation −𝑚𝑔 + 𝑘𝑥0 = 0 signify?

    <p>Restoring force acting upward</p> Signup and view all the answers

    What is the maximum speed of the object undergoing simple harmonic motion with amplitude 0.2 m?

    <p>1.26 m/s</p> Signup and view all the answers

    Which equation correctly represents the velocity of the object at any time t?

    <p>v(t) = -1.26 sin(6.28t)</p> Signup and view all the answers

    What is the maximum magnitude of acceleration for the object with an amplitude of 0.2 m?

    <p>7.90 m/s²</p> Signup and view all the answers

    What is the angular frequency of the object undergoing simple harmonic motion given the force applied?

    <p>1.4 rad/s</p> Signup and view all the answers

    What is the correct expression for the acceleration as a function of time?

    <p>a(t) = -7.89 cos(6.28t)</p> Signup and view all the answers

    What is the period of the simple harmonic motion for the object with a mass of 2.0 kg?

    <p>4.4 s</p> Signup and view all the answers

    When the object is at point P (1.0 m from the center), what is the force acting on it?

    <p>-4.0 N</p> Signup and view all the answers

    What is the speed of the object when it passes through the center of vibration?

    <p>2.4 m/s</p> Signup and view all the answers

    Study Notes

    Simple Harmonic Motion

    • Spring Constant (k): Calculated using k = mg/xo, where m is mass, g is acceleration due to gravity, and xo is the displacement.
    • Period of Oscillation (T): Calculated as T = 1/f, where f is frequency. Also equal to 2π /ω.
    • Angular Velocity (ω): Calculated as ω = 2πf or ω = √(k/m).
    • Amplitude (A): The maximum displacement from the equilibrium position. In this example it is 0.2m.
    • Displacement Function (y(t)): Expressed as y(t) = Acos(ωt), where A is amplitude and ω is angular frequency (angular velocity), and t is time.

    Displacement at Specific Time

    • Displacement at t = 100s: Calculated using y(t) = Acos(ωt), with the calculated values for A and ω.

    Velocity

    • Velocity at Equilibrium: Velocity is maximum when the object is passing through the equilibrium position. Calculated using Vmax = ωA.

    Acceleration

    • Maximum Acceleration: Maximum acceleration is given by Amax = ω²A

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    Physics 2 Assignment - Week 4 Simple Harmonic Motion PDF

    Description

    This quiz covers essential concepts of simple harmonic motion, including calculations for spring constant, period, angular velocity, amplitude, and displacement function. Dive into the relationships between velocity and acceleration in oscillatory motions. Test your understanding of the key principles and formulas governing this fundamental physics topic.

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