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What is the total mechanical energy of a simple harmonic oscillator with a mass

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Question: What is the total mechanical energy of a simple harmonic oscillator with a mass of 1 kg, amplitude of 0.1 m, and spring constant of 100 N/m? (2022)

Options:

  1. 0.5 J
  2. 1 J
  3. 2 J
  4. 4 J

Correct Answer: 1 J

Exam Year: 2022

Solution: 

The total mechanical energy E is given by E = (1/2)kA². Therefore, E = (1/2)(100)(0.1)² = 0.5 J.

What is the total mechanical energy of a simple harmonic oscillator with a mass

Practice Questions

Q1
What is the total mechanical energy of a simple harmonic oscillator with a mass of 1 kg, amplitude of 0.1 m, and spring constant of 100 N/m? (2022)
  1. 0.5 J
  2. 1 J
  3. 2 J
  4. 4 J

Questions & Step-by-Step Solutions

What is the total mechanical energy of a simple harmonic oscillator with a mass of 1 kg, amplitude of 0.1 m, and spring constant of 100 N/m? (2022)
  • Step 1: Identify the formula for total mechanical energy of a simple harmonic oscillator, which is E = (1/2)kA².
  • Step 2: Identify the values given in the problem: mass = 1 kg (not needed for this calculation), amplitude A = 0.1 m, and spring constant k = 100 N/m.
  • Step 3: Substitute the values into the formula: E = (1/2)(100)(0.1)².
  • Step 4: Calculate (0.1)², which is 0.01.
  • Step 5: Multiply 100 by 0.01 to get 1.
  • Step 6: Multiply 1 by (1/2) to get 0.5.
  • Step 7: Conclude that the total mechanical energy E is 0.5 J.
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