For each machine individually ...

$x_1$ starts out as with a maximum positive displacement of 5 at $t=0$. It achieves a max negative displacement of -5 at at $t = \dfrac{1}{100}$ sec (half the period) and back to a max positive displacement of 5 at $t=\dfrac{1}{50}$ sec. This is due to the fact that $x_1$ has the simplified equation of $x_1 = 5\cos(100\pi t)$

$x_2$ achieves a max positive displacement of 6.5 at $t = \dfrac{1}{120}$ sec

Normally, a question like this asks to find the time and value of the max displacement from equilibrium of the superposition, i.e. the sum, of both waves $x_1+x_2$, which would require knowledge of wave addition techniques. As written, question (b) is a bit vague on this point ...