The time period of a particle in simple harmonic motion is $8 \mathrm{~s}$. At $t=0$, it is at the mean…
The time period of a particle in simple harmonic motion is $8 \mathrm{~s}$. At $t=0$, it is at the mean position. The ratio of the distances travelled by it in the first and second seconds is
$\frac{1}{2}$
$\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{2}-1}$
$\frac{1}{\sqrt{3}}$
Solution
Distance $y_1=A \sin \frac{2 \pi}{8} \times 1=\frac{A}{\sqrt{2}}$
and
$y_2=A-\frac{A}{\sqrt{2}}$
The ratio of the distances travelled by it in the first and seconds.
$\frac{y_1}{y_2}=\frac{1}{\sqrt{2}-1}$