Answer
For system 1, the spring constant is 1500 N/m and mass of the block is 500 kg and for system 2, the spring constant is 1200 N/m and mass of the block is 400 kg .
Work Step by Step
In order to maximize the amplitude of oscillations in system 2, the frequency of the system 1 should be equal to the frequency of system 2.
$f_1=f_2$
or, $\frac{1}{2\pi}\sqrt {\frac{k_1}{m_1}}=\frac{1}{2\pi}\sqrt {\frac{k_2}{m_2}}$
or, $\frac{k_1}{m_1}=\frac{k_2}{m_2}$
or, $\boxed{\frac{k_1}{k_2}=\frac{m_1}{m_2}}\;............(1)$
We have to choose springs and blocks from four springs with spring constants k of 1600, 1500, 1400, and 1200 N/m, and four blocks with masses m of 800, 500, 400, and 200 kg.
Among the given springs and bocks, the springs of springs constant 1500 and 1200 N/m and bocks of masses 500 and 400 kg satisfy the equation $1$.
Thus, for system 1, the spring constant is 1500 N/m and mass of the block is 500 kg and for system 2, the spring constant is 1200 N/m and mass of the block is 400 kg .