Correct option is (4) C and D only
\(\vec r = (\hat i + 2 \hat j )A \cos \omega t\)
\(x = A \cos \omega t\)
\(y = 2A \cos \omega t\)
\(y = 2x\)
The path is straight line.
The motion is SHM and periodic as
\(\frac{dr}{dt} = -(\hat i + 2\hat j) \omega A \sin \omega t\)
\(\frac{d^2r}{dt^2} = -(\hat i + 2\hat j) \omega^2 A \cos \omega t\)
\(\vec a = - \omega^2 \vec r\)
