The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts,then the new time period will be

$A$ plank with a small block on top of it is undergoing vertical $SHM$. Its period is $2 \ s$. The minimum amplitude at which the block will separate from the plank is:

The time period of simple harmonic motion of mass $M$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$,where the value of $\alpha$ is . . . . . . .

One end of a long metallic wire of length $L$ is tied to the ceiling. The other end is tied to a massless spring of spring constant $K$. $A$ mass $m$ hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are $A$ and $Y$ respectively. If the mass is slightly pulled down and released,it will oscillate with a time period $T$ equal to

$A$ clock is designed based on the oscillations of a spring-block system suspended vertically in the absence of air resistance. Assume it shows the correct time when a spring of stiffness $k$ and a block of mass $m$ are used. If the block is replaced by another block of mass $4m$,choose the correct option.

$A$ load of mass $m$ falls from a height $h$ onto a scale pan hung from a spring as shown in the figure. If the spring constant is $k$,the mass of the scale pan is zero,and the mass $m$ does not bounce relative to the pan,then the amplitude of vibration is