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Q.

A particle executing SHM with time period ‘T’ is at mean position at time $t_{1} .$ At time $t_{2}$ its KE is 3 times its PE, minimum value of $(t_{2} - t_{1})$ is

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a

$\frac{T}{4}$

b

$\frac{T}{2}$

c

$\frac{T}{6}$

d

$\frac{T}{12}$

answer is A.

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Detailed Solution

$K E = 3 P E$

$\frac{1}{2} m ω^{2} (A^{2} - x^{2}) = 3 (\frac{1}{2} m ω^{2} x^{2})$

$A^{2} - x^{2} = 3 x^{2} (or) 4 x^{2} = A^{2}$

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

Time from x=0 to $x = \frac{A}{2} i s \frac{T}{12}$

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