How quickly does the spring cycle?

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Problem: How quickly does the spring cycle?
A 0.50 kg mass oscillates on a spring with stiffness 200 N/m.
Question: Find its angular frequency.
Givens:
- m = 0.50 kg
- k = 200 N/m
Assumptions: Ideal massless Hookean spring and point mass; no damping; displacement measured from fixed equilibrium.
Choices (LaTeX):
A. 10\ \mathrm{rad\,s^{-1}}
B. 20/(2\pi)\ \mathrm{rad\,s^{-1}}
C. 20\ \mathrm{rad\,s^{-1}}
D. 400\ \mathrm{rad\,s^{-1}}

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.