Question

As shown in the figure, a particle of mass $m=100gm$ is attached with four identical springs, each of length $l=10cm$ . Initial tension in each spring is $F_0=25N$ . Neglecting gravity, calculate the angular frequency (in $rad{s}^{-1}$ ) of small oscillations of the particle along a line perpendicular to the plane of the figure.

Answer 1

Answer: 100

For small $x$ we can assume the tension in each spring to remain constant
$F=-4F_{0}sin\theta \approx -\frac{4F_{0}x}{l}$
$a=-\frac{4F_0}{ml}x$
$\omega =\sqrt{\frac{4F_0}{ml}}=100rad{s}^{-1}$