A mass attached to a spring oscillates with a frequency of 2 Hz. What is the spring constant if the mass is 0.5 kg?

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Q: A mass attached to a spring oscillates with a frequency of 2 Hz. What is the spring constant if the mass is 0.5 kg?

Solution: Using the formula f = (1/2π)√(k/m), we can rearrange to find k = (2πf)²m. Thus, k = (2π(2))²(0.5) = 16 N/m.

Steps: 9

Step 1: Identify the given values. The frequency (f) is 2 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 k. Multiply both sides by 2π: 2πf = √(k/m).
Step 4: Square both sides to eliminate the square root: (2πf)² = k/m.
Step 5: Multiply both sides by m to isolate k: k = (2πf)² * m.
Step 6: Substitute the values of f and m into the equation: k = (2π(2))² * (0.5).
Step 7: Calculate (2π(2))². First, calculate 2π(2) which is approximately 12.5664, then square it to get about 158.0.
Step 8: Multiply the result by 0.5: k = 158.0 * 0.5 = 79.0 N/m.
Step 9: Finalize the answer: The spring constant k is approximately 79.0 N/m.