Question 56: Oscillations

Question

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

Accepted Answer

We know, for an oscillation,
$${V_{\max }} = wA$$ .... (1)
where, A = amplitude
w = frequency of oscillation
and $$w = \sqrt {{k \over m}} $$ .... (2)
from (1) and (2), $${V_{\max }} = \sqrt {{k \over m}} A$$
$$ \Rightarrow {V_{\max }} \propto \sqrt k $$ (As m and A are same (or constant))
$$ \Rightarrow {{{{\left( {{V_{\max }}} \right)}_A}} \over {{{\left( {{V_{\max }}} \right)}_B}}} = \sqrt {{{{k_1}} \over {{k_2}}}} $$
Hence, option 2 is correct.

Answer

$ \sqrt{\frac{k_2}{k_1}} $

Answer

$ \sqrt{\frac{k_1}{k_2}} $

Answer

$ \frac{k_2}{k_1} $

Answer

$ \frac{k_1}{k_2} $

Oscillations

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

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