Question

As shown in the figure, a particle of mass $m=100gm$ is attached with four identical springs, each of length $l=10 \, cm$ . Initial tension in each spring is $F_{0}=25N$ . Neglecting gravity, calculate the angular frequency (in $rads^{- 1}$ ) of small oscillations of the particle along a line perpendicular to the plane of the figure.

Answer 1

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