As shown above, a red ball with a mass of \(2\) kg is fixed on the right end of a spring with its left end fixed on the wall. The above right shows the potential energy \(E\) of the spring as a function of the extension, denoted \(x,\) of the spring (the distance between Point \(O\) and Point \(A\) in the left bottom picture). Which of the following statements is correct?
a) The spring constant of the spring is \(20\) N/m.
b) \(80\) N of force is needed to extend the spring by \(10\) cm.
c) If we extend the spring by \(20\) cm and let it go, the speed of the red ball at Point \(O\) is \(4\) m/s.