a
(a) \(x = 5\sqrt 2 \left( {\sin 2\pi \,t + \cos 2\pi \,t} \right)\)

\( = 5\sqrt 2 \sin 2\pi \,t + 5\sqrt 2 \cos 2\pi \,t\)

\(x = 5\sqrt 2 \sin 2\pi t + 5\sqrt 2 \sin \,\left( {2\pi \,t + \frac{\pi }{2}} \right)\)

Phase difference between constituent waves \(\phi = \frac{\pi }{2}\)

\(\therefore \) Resultant amplitude \(A = \sqrt {{{(5\sqrt 2 )}^2} + {{(5\sqrt 2 )}^2}} =10\, cm.\)