Question

A body executing SHM has its velocity $10cm/s$ and $7cm/s$ when its displacements from mean position are $3cm$ and $4cm$ respectively. The length of path is

• A. $10cm$
• B. $9.5cm$
• C. $4cm$
• D. $11.36cm$

Answer 1

The correct option is D $11.36cm$

$v=\omega \sqrt{A^2-x^2}$
$v_1=10cm/sec$
$v_2=7cm/sec$
$x_1=3cm$
$x_2=4cm$

$v_1=\omega \sqrt{A^2-x_1^2}$

$v_2=\omega \sqrt{A^2-x_2^2}$

$\therefore \frac{10}{7}=\frac{\omega \sqrt{A^2-(3{)}^2}}{\omega \sqrt{A^2-(4{)}^2}}$

$\frac{100}{49}=\frac{A^2-9}{A^2-16}$

$51A^2=1600-(9\times 49)$
$A=4.76cm$
Length of the path is $2A=9.52$ cm