Q. 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 :
Delhi UMET/DPMTDelhi UMET/DPMT 2005Oscillations
Solution:
$v =\omega \sqrt{ A ^{2}- x ^{2}}$
$v _{1}=10\, cm / \sec$
$v _{2}=7\, cm / \sec$
$x _{1}=3\, cm$ $x _{2}=4 cm$
$v _{1}=\omega \sqrt{ A ^{2}- x _{1}^{2}}$
$v _{2}=\omega \sqrt{ A ^{2}- x _{2}^{2}}$
$\frac{100}{49}=\frac{ A ^{2}-9}{ A ^{2}-16}$
$A =4.76\, cm$
Length of the path is $2 A =9.52\, cm$
