Three masses $700 \, g, 500 \, g$,and $400 \, g$ are suspended at the end of a spring as shown and are in equilibrium. When the $700 \, g$ mass is removed,the system oscillates with a period of $3 \, s$. When the $500 \, g$ mass is also removed,it will oscillate with a period of ...... $s$.

An object of mass $2 \,kg$ is attached to a spring with spring constant $8 \,N/m$. If the object is executing simple harmonic motion, then the number of cycles it completes in $66 \,s$ is

$A$ body of mass $1 \ kg$ is suspended from a spring of force constant $600 \ N \ m^{-1}$. Another body of mass $0.5 \ kg$ moving vertically upwards hits the suspended body with a velocity of $3 \ m \ s^{-1}$ and gets embedded in it. The amplitude of motion is (in $cm$)

$A$ particle of mass $1 \, \text{kg}$ is hanging from a spring of force constant $100 \, \text{N/m}$. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period $T$. The time when the kinetic energy and potential energy of the system will become equal is $\frac{T}{x}$. The value of $x$ is ..... .

In a spring-block system as shown in the figure,if the spring constant $K = 9 \pi^2 \ Nm^{-1}$,then the time period of oscillation is (in $s$)

$A$ mass $m_1$ performs $S.H.M.$ with amplitude $A$ while connected to a horizontal spring. While mass $m_1$ is passing through the mean position, another mass $m_2$ $(m_2 < m_1)$ is placed on it so that both masses move together with amplitude $A_1$. The ratio of $A/A_1$ is