The equation of a simple harmonic motion is $X = 0.34 \cos(3000t + 0.74)$,where $X$ and $t$ are in $mm$ and $sec$ respectively. The frequency of the motion is:

Select the wrong statement about simple harmonic motion $(S.H.M.)$.

$A$ particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle after $2T$ time from its initial position is

$A$ particle executing simple harmonic motion along the $Y$-axis has its motion described by the equation $y = A \sin(\omega t) + B$. The amplitude of the simple harmonic motion is

$A$ simple harmonic motion is represented by $\alpha \frac{d^2 x}{d t^2}+\beta x=0$. Its period is

Which of the following functions of time represent $(a)$ simple harmonic motion and $(b)$ periodic but not simple harmonic? Give the period for each case.
$(1)$ $\sin \omega t - \cos \omega t$
$(2)$ $\sin^2 \omega t$