For a mass-spring system with m = 4 kg and k = 40 N/m, what is the angular frequency ω of simple harmonic motion?

For a mass-spring system with m = 4 kg and k = 40 N/m, what is the angular frequency ω of simple harmonic motion?

• A. 3.16 rad/s
• B. 1.58 rad/s
• C. 6.32 rad/s
• D. 10.0 rad/s

Answer: (A)

Angular frequency in a mass-spring system is given by ω = sqrt(k/m). This shows how stiffness and mass influence the oscillation rate: bigger k or smaller m raises ω, making the motion faster. Plugging in k = 40 N/m and m = 4 kg gives ω = sqrt(40/4) = sqrt(10) ≈ 3.16 rad/s. So the angular frequency is about 3.16 rad/s. The other values come from using the wrong ratio or arithmetic, since the correct relation depends on the ratio k/m, not its inverse or a different operation.

Angular frequency in a mass-spring system is given by ω = sqrt(k/m). This shows how stiffness and mass influence the oscillation rate: bigger k or smaller m raises ω, making the motion faster. Plugging in k = 40 N/m and m = 4 kg gives ω = sqrt(40/4) = sqrt(10) ≈ 3.16 rad/s. So the angular frequency is about 3.16 rad/s. The other values come from using the wrong ratio or arithmetic, since the correct relation depends on the ratio k/m, not its inverse or a different operation.