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Oscillations

# A body starting from rest has the following combinations of acceleration, position, velocity and at one instant while its initial displacement is given as the fourth variable. Which of the following combinations describes $SHM$:

$\begin{array}{1 1}(a)\;6,3.5,3,2 \\(b)\;5,4,1,1 \\( c)\; 7,3,2,1 \\(d)\; All\;of\;the\;above \end{array}$

Let $x =\alpha+ A \sin w t$ be the equation of SHM.
Then $velocity = Aw \cos wt$ & $acceleration =-Aw^2 \sin wt$ calculate $A \sin wt$ using current position & initial position.
Using equation for acceleration you can find $w^2$.
It will turn out to be negative for all the three cases which makes w to be imaginary which is not possible in an SHM.
Thus 'd' is right.