Question

Two identical point masses P and Q, suspended from two separate massless springs of spring constants k₁ and k₂, respectively, oscillate vertically. If their maximum speeds are the same, the ratio (A_Q/A_P) of the amplitude A of mass Q to the amplitude Ap of mass P is:

Options

• `(k_2)/(k_1)`

• `(k_1)/(k_2)`

• `sqrt((k_2)/(k_1))`

• `sqrt((k_1)/(k_2))`

Answer 1

`sqrt((k_1)/(k_2))`

Explanation:

`v_(1(max)) = v_(2(max))`

A₁ω₁ =  A₂ω₂

`A_1sqrt(k_1/m) = A_2sqrt(k_2/m)`

`A_2/A_1 = sqrt((k_1)/(k_2))`

`A_Q/A_P = sqrt((k_1)/(k_2))`