Two damped spring-mass oscillating systems have identical spring constants and decay times. However, system $A's$ mass $m_A$ is twice system $B's$ mass $m_B$ . How do their damping constants, $b$ , compare ?
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You are holding a shallow circular container of radius $R$, filled with water to a height $h ( h < < R )$. When yon walk with speed $v$, it is seen that water starts spilling over. This happens due to the resonance of the periodic impulse given to the container (due to walking) with the oscillation of the water in the container. If the time period of water oscillating in the container is inversely proportional to $\sqrt{ h }$, then $v$ is proportional to
Two springs of force constants $300\, N / m$ (Spring $A$) and $400$ $N / m$ (Spring $B$ ) are joined together in series. The combination is compressed by $8.75\, cm .$ The ratio of energy stored in $A$ and $B$ is $\frac{E_{A}}{E_{B}} .$ Then $\frac{E_{A}}{E_{B}}$ is equal to
Two pendulums have time periods $T$ and $5T/4.$ They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum they will be again in the same phase :
Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $K$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The amplitude of oscillations is