$A$ spring-mass system vibrates such that the mass travels on a surface with a coefficient of friction $\mu$. The mass is released after compressing the spring by a distance $a$ and it travels up to a distance $b$ after its equilibrium position. Then,while traveling from $x = -a$ to $x = b$,the reduction in its amplitude will be:

Three blocks of masses $700 \,g$,$500 \,g$,and $400 \,g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $700 \,g$ block is removed,the system has a period of oscillation of $3 \,s$. If both $700 \,g$ and $500 \,g$ blocks are removed,the period of oscillation becomes

$A$ block $P$ of mass $m$ is placed on a frictionless horizontal surface. Another block $Q$ of the same mass $m$ is kept on $P$ and connected to a wall with the help of a spring of spring constant $k$ as shown in the figure. $\mu_s$ is the coefficient of static friction between $P$ and $Q$. The blocks move together performing simple harmonic motion $(SHM)$ of amplitude $A$. The maximum value of the friction force between $P$ and $Q$ is

Two identical springs of constant $k$ are connected in series and then in parallel. $A$ mass $m$ is suspended from them,the ratio of their frequencies of vertical oscillations will be

As per the given figures,two springs of spring constants $K$ and $2K$ are connected to a mass $m$. If the period of oscillation in figure $(a)$ is $3 \text{ s}$,then the period of oscillation in figure $(b)$ will be $\sqrt{x} \text{ s}$. The value of $x$ is $.........$

$A$ mass $m$ attached to a spring oscillates every $2 \, s$. If the mass is increased by $2 \, kg$,then the time period increases by $1 \, s$. The initial mass is ..... $kg$.