Equation of first simple harmonic motion, x1=5‌sin(2πt+
Ï€
4
). Equation of second simple harmonic motion, x2=5√2(sin‌2‌π‌t+cos‌2‌π‌t) Simplifying the second equation of simple harmonic motion asfollows
x2=5√2(sin‌2‌π‌t×
1
√2
+cos‌2‌π‌t×
1
√2
)√2
=10(sin‌2‌π‌t‌cos‌
Ï€
4
+cos‌2‌π‌t‌sin‌
Ï€
4
) =10‌sin(2πt+
Ï€
4
) The ratio of amplitudes of two simple harmonic motions is
A2
A1
=
10
5
=2 Thus, amplitude of second motion is 2 times the amplitude in first motion.