The time period of oscillation for the given combination will be:

$A$ mass $M$ is suspended from a light spring. An additional mass $M_1$ added extends the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period $T=$

$A$ spring of unstretched length $l$ has a mass $m$ with one end fixed to a rigid support. Assuming the spring to be made of a uniform wire,the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is

For the system given below,find the angular frequency of oscillation.

The potential energy of a particle of mass $0.1\,kg,$ moving along the $x-$axis,is given by $U = 5x(x-4)\,J,$ where $x$ is in metres. It can be concluded that

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 $\,s$)