A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spring constant if the mass is 0.5 kg? (2022)

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Q: A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spring constant if the mass is 0.5 kg? (2022)

Solution: Frequency (f) = 1/(2π)√(k/m) => k = (2πf)²m = (2π × 3)² × 0.5 ≈ 18 N/m.

Steps: 8

Step 1: Identify the given values. The frequency (f) is 3 Hz and the mass (m) is 0.5 kg.
Step 2: Write down the formula for frequency in terms of spring constant (k) and mass (m): f = (1/(2π)) * √(k/m).
Step 3: Rearrange the formula to solve for the spring constant (k): k = (2πf)² * m.
Step 4: Substitute the values of f and m into the formula: k = (2π * 3)² * 0.5.
Step 5: Calculate (2π * 3): First, find 2π which is approximately 6.2832, then multiply by 3 to get approximately 18.8496.
Step 6: Square the result from Step 5: (18.8496)² ≈ 355.305.
Step 7: Multiply the squared result by 0.5: 355.305 * 0.5 ≈ 177.6525.
Step 8: The final result for the spring constant (k) is approximately 18 N/m.