A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical xy-plane having equatioin `x^(2)`=5y(x,y are in meter). After slight displacement, the particle is set free. Find angular frequency of osciallation (in rad/sec) (Take g=10 m/`s^(2))`

Answer

2

Explanation

Energy
` E=(1)/(2)mv^(2)+mgy=(1)/(2)mv^(2)+mg((x^(2))/(5))`
For `(dE)/(dt)=0,a=-((g)/(2.5))x`
SO `omega=((g)/(2.5))^(1//2)=((10)/(2.5))^(1//2)=1rad//sec`