All four methods should yield the same result if implemented correctly. However, the most accurate method depends on various factors, such as the complexity of the system, the accuracy of the input parameters, and the computational resources available.
For a simple system like a single bar with fixed support, the analytical and lumped parameter methods are straightforward and can provide accurate results with minimal computational resources.
The FEM approach and commercial software like ANSYS can provide more accurate results for complex systems with varying material properties, geometric shapes, and boundary conditions. However, they require more computational resources and expertise to implement correctly.
Therefore, for the given system of a single bar with fixed support, the analytical and lumped parameter methods are sufficient and provide accurate results. The first natural frequency of longitudinal vibration of the single bar is 225.3 Hz.
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