**Introduction to Damped Mechanical Systems**A damped mechanical system is shown in the figure below. The system has a spring constant (k) of \(2 \times 10^4 \, \text{N/m}\) and a mass (m) of 2 kg. It is subject to a sinusoidal driving force with a drive frequency of 10 Hz. The amplitude of the transient motion decreases 100 times after 10 drive periods. Your task is to answer the following questions:1. What is the damping constant?2. What is the frequency of the transient motion?3. What is the amplitude of the driving force if the amplitude of the long-term oscillations is 0.1 m?**Details Provided:**- Spring constant, \(k = 2 \times 10^4 \, \text{N/m}\)- Drive frequency, \(\text{drive freq} = 10 \, \text{Hz}\)**Diagram of the System:**The diagram illustrates a simple mass-spring system with damping:```[ Ceiling ] | | --- / k \| || m ||_____| ```**Further Exploration: Resonance Frequency**In the second part of the analysis, determine the following:1. What is the frequency of resonance of the mechanical system?2. What is the amplitude of oscillations at the resonance?**Diagram Repeated for Reference:**The diagram signifies the same mass-spring setup as before.---With this information, you can explore the concepts of damping, transient motion, and resonance in mechanical systems.

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