A simple harmonic oscillator has a mass of 0.5 kg and a spring constant of 200 N/m. What is the angular frequency of the oscillator?

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Q: A simple harmonic oscillator has a mass of 0.5 kg and a spring constant of 200 N/m. What is the angular frequency of the oscillator?

Solution: The angular frequency ω is given by the formula ω = √(k/m). Here, k = 200 N/m and m = 0.5 kg. Thus, ω = √(200/0.5) = √400 = 20 rad/s.

Steps: 6

Step 1: Identify the values given in the problem. The mass (m) is 0.5 kg and the spring constant (k) is 200 N/m.
Step 2: Write down the formula for angular frequency (ω) of a simple harmonic oscillator, which is ω = √(k/m).
Step 3: Substitute the values of k and m into the formula. This means you will calculate √(200/0.5).
Step 4: Calculate the value of 200 divided by 0.5. This equals 400.
Step 5: Now, take the square root of 400. The square root of 400 is 20.
Step 6: Therefore, the angular frequency (ω) is 20 rad/s.