A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K _1$ and $K _2$. For the frictionless surface, the time period of oscillation of mass $m$ is
$\frac{1}{2 \pi} \sqrt{\frac{ K _1+ K _2}{ m }}$
$\frac{1}{2 \pi} \sqrt{\frac{ K _1- K _2}{ m }}$
$2 \pi \sqrt{\frac{ m }{ K _1+ K _2}}$
$2 \pi \sqrt{\frac{m}{K_1-K_2}}$
A spring having a spring constant $‘K’$ is loaded with a mass $‘m’$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is
If two similar springs each of spring constant $K _{1}$ are joined in series, the new spring constant and time period would be changed by a factor
Spring of spring constant $1200\, Nm^{-1}$ is mounted on a smooth frictionless surface and attached to a block of mass $3\, kg$. Block is pulled $2\, cm$ to the right and released. The angular frequency of oscillation is .... $ rad/sec$
A mass of $5\, {kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4\, {m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In ${m} / {s}^{2}$)
A particle executes $SHM$ with amplitude of $20 \,cm$ and time period is $12\, sec$. What is the minimum time required for it to move between two points $10\, cm$ on either side of the mean position ..... $\sec$ ?