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Q.
A particle is in a linear SHM. If the acceleration and the corresponding velocity of this particle are ' $a$ ' and ' $v$ ', then the graph relating to these values is
Oscillations
Solution:
The equation giving relation between acceleration and speed as function of distance from mean position
is $a=-\omega^{2} x $ .....(i)
$v=\omega \sqrt{a^{2}-x^{2}}$ .....(ii)
from equation (i) and (ii) we get
$a^{2}=\omega^{4}\left(A^{2}-\frac{v^{2}}{\omega^{2}}\right)$