Which of the following expressions corresponds to simple harmonic motion along a straight line,where $x$ is the displacement and $a, b, c$ are positive constants?

Which of the following functions of time represent $(a)$ simple harmonic,$(b)$ periodic but not simple harmonic,and $(c)$ non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):
$(a)$ $\sin \omega t - \cos \omega t$
$(b)$ $\sin^3 \omega t$
$(c)$ $3 \cos (\pi/4 - 2 \omega t)$
$(d)$ $\cos \omega t + \cos 3 \omega t + \cos 5 \omega t$
$(e)$ $\exp(-\omega^2 t^2)$
$(f)$ $1 + \omega t + \omega^2 t^2$

$A$ point particle of mass $0.1 \ kg$ is executing $S.H.M.$ with an amplitude of $0.1 \ m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \ J$. Obtain the equation of motion of this particle if the initial phase of oscillation is $45^{\circ}$.

$A$ simple harmonic motion is represented by $F(t) = 10\sin(20t + 0.5)$. The amplitude of the $S.H.M.$ is $a = $ ....

How many amplitudes does a Simple Harmonic Oscillator $(SHO)$ cover in half of its time period?

Mark the wrong statement.