Below are sets of values for the spring constant $k,$ damping constant $b,$ and mass $m$ for a particle in damped harmonic motion. Which of the sets takes the longest time for its mechanical energy to decrease to one$-$fourth of its initial value?

$4k_0,b_0,2m_0$

$\frac{k_0}{2},6b_0,2m_0$

$k_0,b_0,10m_0$

$3k_0,2b_0,m_0$

$k_0,b_0,m_0$