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

Question

A body executing SHM has its velocity 10 cm/s and 7 cm/s, when its displacements from the mean position are 3 cm and 4 cm, respectively The length of path is : (A) 10 cm (B) 9.5 cm (C) 4 cm (D) 11.36 cm

Tardigrade Admin · Accepted Answer

v =ω √ A 2- x 2 v 1=10 cm / sec v 2=7 cm / sec x 1=3 cm x 2=4 cm v 1=ω √ A 2- x 12 v 2=ω √ A 2- x 22 (100/49)=( A 2-9/ A 2-16) A =4.76 cm Length of the path is 2 A =9.52 cm

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

10 cm

9.5 cm

4 cm

11.36 cm

$v = ω A^{2} - x^{2}$
$v_{1} = 10 c m / sec$
$v_{2} = 7 c m / sec$
$x_{1} = 3 c m$ $x_{2} = 4 c m$
$v_{1} = ω A^{2} - x_{1}^{2}$
$v_{2} = ω A^{2} - x_{2}^{2}$
$\frac{100}{49} = \frac{A ^{2} - 9}{A ^{2} - 16}$
$A = 4.76 c m$
Length of the path is $2 A = 9.52 c m$

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