(Solved): The uniform rod of mass \( m \) is supported by a pin at \( A \) and a spring at \( B \). \( B \) ...

The uniform rod of mass \( m \) is supported by a pin at \( A \) and a spring at \( B \). \( B \) is given a small sideward displacement and released. (Figure 1) Figure 1 of 1 Part A Determine the natural period of vibration. Express your answer in terms of \( \pi \), acceleration due to gravity \( g \), some or all of the variables \( m, k \), and \( L \).