A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spr

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Question: A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spring constant if the mass is 2 kg? (2023)

Options:

Correct Answer: 18 N/m

Exam Year: 2023

Solution:

Frequency (f) = (1/2π)√(k/m) => k = (2πf)² * m = (2π*3)² * 2 ≈ 18 N/m.

A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spring constant if the mass is 2 kg? (2023)

A mass attached to a spring oscillates with a frequency of 3 Hz. What is the spring constant if the mass is 2 kg? (2023)

Step 1: Identify the given values. The frequency (f) is 3 Hz and the mass (m) is 2 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 * 2.
Step 5: Calculate (2π*3): First, calculate 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 the mass (2 kg): k ≈ 355.305 * 2 ≈ 710.61 N/m.
Step 8: Finalize the calculation: The spring constant k is approximately 710.61 N/m.

Simple Harmonic Motion – The question tests understanding of the relationship between frequency, mass, and spring constant in oscillatory motion.
Spring Constant Calculation – It assesses the ability to manipulate the formula for frequency in terms of mass and spring constant.