JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Elasticity & SHM

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1 kg, the angular frequency is

ω_{1}

. When the mass block is 2 kg the angular frequency is

ω_{2}

. The ratio

ω_{2} / ω_{1}

is :

Answer: (B)

Solution

For a block on a frictionless surface attached to a spring of stiffness

k

, the angular frequency is

ω = \frac{k}{m}

, so for an unchanged spring

ω \propto \frac{1}{m}

. Going from

m_{1} = 1

kg to

m_{2} = 2

kg,

\frac{ω _{2}}{ω _{1}} = \frac{m _{1}}{m _{2}} = \frac{1}{2} = \frac{1}{2}

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Single correct option