When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion is described by $y ( t )= y _{0} \sin ^{2} \omega t ,$ where $'y'$ is measured from the lower end of unstretched spring. Then $\omega$ is
When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion is described by $y ( t )= y _{0} \sin ^{2} \omega t ,$ where $'y'$ is measured from the lower end of unstretched spring. Then $\omega$ is
- [JEE MAIN 2020]
- A
$\sqrt{\frac{g}{y_{0}}}$
- B
$\sqrt{\frac{g}{2 y_{0}}}$
- C
$\frac{1}{2} \sqrt{\frac{g}{y_{0}}}$
- D
$\sqrt{\frac{2 g}{y_{0}}}$
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$(a)$ the period of oscillation.
$(b)$ the maximum speed and
$(c)$ maximum acceleration of the collar.