**Category:** Mechanics  
**Subtype:** Oscillations and Resonance  
**Problem Description:** This problem is about forced oscillations and resonance in a mechanical system. It asks which condition leads to resonance occurring when a system is subjected to a periodic external force.  

**Key Concepts:**  
- Forced oscillations: When an external force drives a system to oscillate.  
- Resonance: A phenomenon that occurs when the frequency of the external force matches the natural frequency of the system, leading to a significant increase in amplitude.  

**Options Analysis:**  
- A. The frequency of the external force equals the natural frequency of the system.  
- B. The amplitude of the external force is much smaller than the natural amplitude of the system.  
- C. The period of the external force is shorter than the period of the natural oscillation of the system.  
- D. The amplitude of the external force equals the natural amplitude of the system.  

The problem requires identifying the correct condition for resonance from the given options.