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A body has the following combinations of acceleration, position, velocity at one instant while the fourth parameter is its initial position. Which of the following combinations describes $SHM$:

$\begin{array}{1 1}(a)\;9,3.5,3,.5 \\(b)\;5,4,1,0 \\( c)\; 7,3,2,9 \\(d)\;2,3,2,7 \end{array}$

1 Answer

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.
Hence 'a' is the correct answer
answered Dec 11, 2013 by meena.p

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