Question

A particle of mass ${}^{\prime }{m}^{\prime }$ is attached to three identical springs $A,B$ and $C$ each of force constant ${}^{\prime }{k}^{\prime }$ as shown in figure. If the particle of mass ${}^{\prime }{m}^{\prime }$ is pushed sightly against the spring ${}^{\prime }{A}^{\prime }$ and released. Find the period of oscillation.

Answer 1

$F_{net}=F_A+F_B\cos {45}^0+F_C\cos {45}^0$

$=ky+2k{y}^{\prime }\cos {45}^0=ky+2k\left(y\cos {45}^0\right)\cos {45}^0=2ky$

$F_{net}=k^{\prime }y\Rightarrow k^{\prime }y=2ky\Rightarrow k^{\prime }=2k$

$T=2\pi \sqrt{\frac{m}{k^{\prime }}}=2\pi \sqrt{\frac{m}{2k}}$

we get, period of oscillation is $2\pi \sqrt{\frac{m}{2k}}.$