Can the function `f(t)=sinomegat+cosomegat,` represent the simple harmonic function? Explain.

Explanation

The function, `f(t)=sinomegat+cosomegat`
or `f(t)=sqrt(2)((1)/(sqrt(2))sinomegat+(1)/(sqrt(2))cosomegat)`
`=sqrt(2)(cos((pi)/(4))sinomegat+sin((pi)/(4))cosomegat)`
`=sqrt(2)sin(omegat+(pi)/(4))=sqrt(2)sin(omegat+(pi)/(4)+2pi)`
`=sqrt(2)sin[omegat(t+(2pi)/(omega))+(pi)/(4)]`
This, represents a simple harmonic motion with period `2pi//omega`.