Question: Structural dynamics is critical in earthquake engineering for assessing the seismic response of buildings and infrastructure. Explain the principles of structural dynamics and their importance in predicting the behavior of structures under earthquake loading. Discuss the concept of natural frequency, damping, and resonance in structural systems, emphasizing their role in determining the dynamic response characteristics of buildings and bridges. Analyze the methods used for seismic analysis and design, including response spectrum analysis and time history analysis, and their application in evaluating structural performance. Provide examples of how engineers incorporate structural dynamics theory to enhance the seismic resilience of civil infrastructure, ensuring public safety and minimizing earthquake$-$induced damage.