已知F1,F2分别表示下面两个函数:f1=sin(πt/3+π/4),f2=√3sin(πt/3-π/4),求复合函数f1+f2的振幅,周期,频率及初相

Question

已知F1,F2分别表示下面两个函数:f1=sin(πt/3+π/4),f2=√3sin(πt/3-π/4),求复合函数f1+f2的振幅,周期,频率及初相

Answer 1

f1=sin(π/3t+π/4),
f2=√3sin(π/3t-π/4) =√3sin(π/3t+π/4-π/2)
=-√3cos(π/3t+π/4)
f1+f2=sin(π/3t+π/4)-√3cos(π/3t+π/4)
=2sin((π/3t+π/4)-π/3)
=2sin(π/3t-π/12)
=2sin(π/3t+23π/12)
故振幅是2,周期是6,初相是23π/12,频率是1/6