A block of mass \(m\) is attached to an ideal spring on a frictionless horizontal surface. The spring is modified such that its effective spring constant increases linearly with time according to \(k(t) = k_0 + bt\), where \(k_0\) and \(b\) are positive constants. Which of the following correctly pairs the instantaneous rate of change of the block's angular frequency \(\left.\dfrac{d\omega}{dt}\right|_{t=0}\) at time \(t = 0\) with the qualitative trend of the oscillation period \(T(t)\) as time increases?