Problem: A child on a swing has a natural period of 2 seconds. How often should the child push the swing to achieve resonance? Solution: 1. Identify the natural period (T): The problem states the swing takes 2 seconds to complete one full cycle (back and forth). 2. Understand Resonance Condition: Resonance occurs when the driving force (the push) matches the natural frequency of the system. 3. Calculate Frequency (f): Frequency is the reciprocal of the period. Formula: f = 1/T. 4. Substitute values: f = 1 / 2 seconds. 5. Calculate result: f = 0.5 Hz. Conclusion: The child should push the swing once every 2 seconds to achieve resonance and go higher.