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When a body is in SHM then match the following
List I List II
A) Velocity is maximum i) At half of the amplitude
B) K.E. is 3/4^th of total energy ii) At the mean position
C) P.E. is 3/4^th of total energy iii) At the extreme position
D) Acceleration is maximum iv) At $\frac{\sqrt{3}}{2}$ times the amplitude
A B C D
(1) ii i iv iii
(2) ii i iii iv
(3) i ii iv iii
(4) i ii iii iv

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answer is A.

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Detailed Solution

$velocity is maximum at the mean position$

$Kinetic is 3 / 4 th of total energy means potential energy is 1 / 4 th of total energy$

$from the defintion of P . E and total energy$

$\frac{1}{2} {mω}^{2} x^{2} = \frac{1}{4} (\frac{1}{2} {mω}^{2} A^{2})$

$x^{2} = \frac{A^{2}}{4}$

$x = \pm \frac{A}{2}$

$Potential energy is 3 / 4 th of total energy$

$\frac{1}{2} {mω}^{2} x^{2} = \frac{3}{4} (\frac{1}{2} {mω}^{2} A^{2})$

$x = \pm \frac{\sqrt{3}}{2} A$

maximum acceleration is at the extreme position

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