For the experiment done in lab, recall that applying \(\Sigma F_x = ma_x\) to the ball gives the equation \(F_{string} = m4\pi^2f^2L\). Combine this result with the result of applying \(\Sigma F_y = ma_y\) and derive an equation for \(\sin \theta\) in terms of \(f\) and \(L\). \(\theta\) is the angle between the string and the horizontal.
(a) For a given \(L\), does the angle \(\theta\) increase, decrease, or stay the same as \(f\) is increased?
\(\circ\) increase
\(\circ\) decrease
\(\circ\) stay the same
(b) For \(L = 50.0\) cm and \(f = 1.15\) rev/s, what is the angle \(\theta\)? (Use \(g = 9.80\) m/s².)