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A simple harmonic oscillator has a mass of 2 kg and a spring constant of 200 N/m

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Question: A simple harmonic oscillator has a mass of 2 kg and a spring constant of 200 N/m. What is the angular frequency of the oscillator?

Options:

  1. 5 rad/s
  2. 10 rad/s
  3. 20 rad/s
  4. 15 rad/s

Correct Answer: 10 rad/s

Solution: 

The angular frequency Ο‰ is given by the formula Ο‰ = √(k/m). Here, k = 200 N/m and m = 2 kg. Thus, Ο‰ = √(200/2) = √100 = 10 rad/s.

A simple harmonic oscillator has a mass of 2 kg and a spring constant of 200 N/m

Practice Questions

Q1
A simple harmonic oscillator has a mass of 2 kg and a spring constant of 200 N/m. What is the angular frequency of the oscillator?
  1. 5 rad/s
  2. 10 rad/s
  3. 20 rad/s
  4. 15 rad/s

Questions & Step-by-Step Solutions

A simple harmonic oscillator has a mass of 2 kg and a spring constant of 200 N/m. What is the angular frequency of the oscillator?
  • Step 1: Identify the formula for angular frequency, which is Ο‰ = √(k/m).
  • Step 2: Note the values given: the spring constant k is 200 N/m and the mass m is 2 kg.
  • Step 3: Substitute the values into the formula: Ο‰ = √(200/2).
  • Step 4: Calculate the value inside the square root: 200 divided by 2 equals 100.
  • Step 5: Take the square root of 100, which is 10.
  • Step 6: Conclude that the angular frequency Ο‰ is 10 rad/s.
  • Simple Harmonic Motion – The study of oscillatory motion where the restoring force is proportional to the displacement from equilibrium.
  • Angular Frequency – A measure of how quickly an object oscillates, calculated using the formula Ο‰ = √(k/m).
  • Spring Constant – A measure of the stiffness of a spring, represented by k in Hooke's law.
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