Energy Conservation in SHM Quiz with Answers: Test Your Knowledge

📚 Quick Study Guide

• 🎢 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.
• 🧮 Formula for Potential Energy (PE): $PE = \frac{1}{2} kx^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.
• 💪 Formula for Kinetic Energy (KE): $KE = \frac{1}{2} mv^2$, where $m$ is the mass and $v$ is the velocity.
• 🎯 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.
• ⏰ Period (T): The time for one complete oscillation. For a mass-spring system: $T = 2\pi \sqrt{\frac{m}{k}}$.
• 📐 Frequency (f): The number of oscillations per unit time: $f = \frac{1}{T}$.
• 📍 Amplitude (A): The maximum displacement from the equilibrium position.

🧪 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