A horizontal spring-mass system oscillates with a frequency of 0.40 Hz. What is the spring constant if the mass is 0.5 kg?

• A. 0.32 N/m
• B. 5.00 N/m
• C. 1.26 N/m
• D. 3.16 N/m

Answer: (D)

Verified step by step guidance

1. Start by recalling the formula for the frequency of a spring-mass system: \( f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \), where \( f \) is the frequency, \( k \) is the spring constant, and \( m \) is the mass.
2. Rearrange the formula to solve for the spring constant \( k \): \( k = (2\pi f)^2 m \).
3. Substitute the given values into the equation: \( f = 0.40 \text{ Hz} \) and \( m = 0.5 \text{ kg} \).
4. Calculate \( (2\pi f)^2 \) to find the factor by which the mass is multiplied to get the spring constant.
5. Multiply the result from the previous step by the mass \( m = 0.5 \text{ kg} \) to find the spring constant \( k \).