Question

A particle is executing SHM with a time period of 8 sec. If starts from the mean position at time t=0, the ratio of distances covered by it in 1st and a 2nd second are:

• A. 1
• B. $1/(\sqrt{2}-1)$
• C. $1/\left(\sqrt{3-1}\right)$
• D. $\sqrt{2-1}$

Answer 1

The correct option is B $1/(\sqrt{2}-1)$

angular velocity of the particle is $\frac{2\pi }{T}=\frac{2\pi }{8}=\frac{\pi }{4}$

in first sec it move at a angle $\frac{\pi }{4}$

if we take a projection of circular path on the axis of is $\frac{1}{\sqrt{2}}$

in another second sec it move at a another $\frac{\pi }{4}$

it distance at the axis $1-\frac{1}{\sqrt{2}}$

ratio of distance in first second and in 2 second $\frac{\frac{1}{\sqrt{2}}}{1-\frac{1}{\sqrt{2}}}$

$=\frac{1}{\sqrt{2}-1}$

hence the option is B is correct