The scale of a spring balance which can measure from $0$ to $15 \ kg$ is $0.25 \ m$ long. If a body suspended from this balance oscillates with a time period $\frac{2 \pi}{5} \ s$,neglecting the mass of the spring,find the mass of the body suspended. (in $kg$)

As shown in the figure, a block of weight $20 \,N$ is connected to the top of a smooth inclined plane by a massless spring of constant $8 \pi^2 \,Nm^{-1}$. If the block is pulled slightly from its mean position and released, the period of oscillations is (Acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,s$)

$A$ block of mass $m$ rests on a platform. The platform is given up and down $SHM$ with an amplitude $d$. What is the maximum frequency so that the block never leaves the platform?

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 vibration is

In an oscillating spring-mass system,a spring is connected to a box filled with sand. As the box oscillates,sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system change with time $t$. Which one of the following options schematically depicts these changes correctly?

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended,the period of oscillation will now be