Question

Two bodies A and B of equal mass are suspended from two separate massles springs of force constant k₁ and k₂, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body A to that of body B is ______.

Options

• `sqrt("k"_2/"k"_1)`

• `"k"_2/"k"_1`

• `"k"_1/"k"_2`

• `sqrt("k"_1/"k"_2)`

Answer 1

Two bodies A and B of equal mass are suspended from two separate massles springs of force constant k₁ and k₂, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body A to that of body B is `underline(sqrt("k"_2/"k"_1))`.

Explanation:

The maximum velocity of body in SHM,

v = Aω

where, A is amplitude of body and ω is the angular frequency.

It is given that, the maximum velocities of bodies are equal.

`"v"_"A" = "v"_"B"`

`"A"_"A" omega_"A" = "A"_"B" omega_"B"`

`"A"_"A"sqrt("k"_1/"m") = "A"_"B" sqrt("k"_2/"m")   ...(because omega = sqrt("k"/"m"))`

`"A"_"A"/"A"_"B" = sqrt("k"_2/"k"_1)`