Question 32: Oscillations

Question

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k
1
and k
2
, 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 k 1 and k 2 , 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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