william.potts
william.potts 7h ago โ€ข 0 views

Energy Conservation in SHM Quiz with Answers: Test Your Knowledge

Hey everyone! ๐Ÿ‘‹ Getting ready for your physics exams? Let's test your knowledge of Simple Harmonic Motion (SHM) and energy conservation! This quick guide and quiz will help you ace those problems. Good luck! ๐Ÿ‘
โš›๏ธ Physics

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๐Ÿ“š Quick Study Guide

  • ๐ŸŽข Definition: Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
  • ๐Ÿงฎ Formula for Potential Energy (PE): $PE = \frac{1}{2} kx^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.
  • ๐Ÿ’ช Formula for Kinetic Energy (KE): $KE = \frac{1}{2} mv^2$, where $m$ is the mass and $v$ is the velocity.
  • ๐ŸŽฏ Total Energy (E): In SHM, the total energy is conserved and is the sum of potential and kinetic energy: $E = PE + KE = \frac{1}{2}kA^2$, where $A$ is the amplitude.
  • โฐ Period (T): The time for one complete oscillation. For a mass-spring system: $T = 2\pi \sqrt{\frac{m}{k}}$.
  • ๐Ÿ“ Frequency (f): The number of oscillations per unit time: $f = \frac{1}{T}$.
  • ๐Ÿ“ Amplitude (A): The maximum displacement from the equilibrium position.

๐Ÿงช Practice Quiz

  1. Which of the following statements is true regarding energy conservation in SHM?
    1. A. Total energy increases over time.
    2. B. Potential energy is always equal to kinetic energy.
    3. C. Total energy remains constant if no external forces act.
    4. D. Kinetic energy is always greater than potential energy.
  2. A mass-spring system has a spring constant of $k = 100$ N/m and an amplitude of $A = 0.1$ m. What is the total energy of the system?
    1. A. 0.5 J
    2. B. 1 J
    3. C. 2 J
    4. D. 0 J
  3. At what point in the SHM cycle is the kinetic energy maximum?
    1. A. At the maximum displacement.
    2. B. At the equilibrium position.
    3. C. When the potential energy is maximum.
    4. D. Halfway between the equilibrium and maximum displacement.
  4. If the amplitude of an SHM is doubled, what happens to the total energy?
    1. A. It remains the same.
    2. B. It doubles.
    3. C. It quadruples.
    4. D. It halves.
  5. A 0.5 kg mass is attached to a spring with a spring constant of 200 N/m. What is the potential energy when the displacement is 0.05 m?
    1. A. 0.125 J
    2. B. 0.25 J
    3. C. 0.5 J
    4. D. 1 J
  6. Which of the following affects the period of a simple pendulum in SHM?
    1. A. Mass of the bob.
    2. B. Amplitude of the swing.
    3. C. Length of the pendulum.
    4. D. Initial velocity.
  7. In an ideal SHM system, when potential energy is at its maximum, what is the kinetic energy?
    1. A. Maximum
    2. B. Half of the maximum potential energy
    3. C. Zero
    4. D. Equal to the potential energy
Click to see Answers
  1. C
  2. A
  3. B
  4. C
  5. B
  6. C
  7. C

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