A mass on a horizontal spring has k = 16 N/m and m = 4 kg. What is the natural frequency f?

A mass on a horizontal spring has k = 16 N/m and m = 4 kg. What is the natural frequency f?

• A. 0.32 Hz
• B. 3.2 Hz
• C. 0.16 Hz
• D. 1.28 Hz

Answer: (A)

A mass on a spring vibrates at a frequency determined by how stiff the spring is and how heavy the mass is. For a simple mass-spring system, the angular frequency is ω = sqrt(k/m) and the regular frequency is f = ω/(2π). Plugging in k = 16 N/m and m = 4 kg gives k/m = 4 s^-2, so ω = sqrt(4) = 2 rad/s. Then f = 2/(2π) = 1/π ≈ 0.318 Hz, which is about 0.32 Hz. This matches the given value.

A mass on a spring vibrates at a frequency determined by how stiff the spring is and how heavy the mass is. For a simple mass-spring system, the angular frequency is ω = sqrt(k/m) and the regular frequency is f = ω/(2π).

Plugging in k = 16 N/m and m = 4 kg gives k/m = 4 s^-2, so ω = sqrt(4) = 2 rad/s. Then f = 2/(2π) = 1/π ≈ 0.318 Hz, which is about 0.32 Hz. This matches the given value.