Question

A particle is performing $SHM$ having position $x$ = $A\; cos\; 30°$, and $A\; = 40 \;cm$. If its kinetic energy at this position is $200 \;J$, the value of force constant in $(kN/m)$ is?

Answer 1

$x=40\times\frac{\sqrt3}{2}=20\sqrt3 \,cm\,as\,\omega=\sqrt{\frac{K}{M}}$

$\frac{1}{2}mv^2=\frac{1}{2}m\omega^2=(A^2-x^2)=200$

$\frac{1}{2}\times m\times \frac{K}{m}(0.16-0.12)=200$

$k=\frac{400}{0.04}=10000$ N/m

$\text{The correct answer is 10 kN/m.}$