Two simple harmonic motions are represented by the equations: x_(1)=5sin(2pit+(pi)/(4)),x^(2)=5sqrt(2)(sin2pit+cos2pit) What is the ratio of their amplitudes?

Two simple harmonic motions are represented by the equations: x_(1)=5

1.	Two simple harmonic motions are represented by the equations: x_(1)=5sin(2pit+(pi)/(4)),x^(2)=5sqrt(2)(sin2pit+cos2pit) What is the ratio of their amplitudes?
Answer» Solution :`x_(1)=5SIN(2pit+(pi)/(4))""[therefore A_(1)=5]` `x_(2)=5sqrt(2)(sin2pit+cos2pit)` `=10sin(sin2pitcos.(pi)/(4)+cos2pitsin.(pi)/(4))` `x_(2)=10sin(2pit+(pi)/(4))""[therefore A_(2)=10]` Hence, `(A_(1))/(A_(2))=(5)/(10)=1:2` `A_(1):A_(2)=1:2`