The potential energy of a particle of mass $100 \,g$ moving along the $x$-axis is given by $U = 5x(x - 4)$,where $x$ is in metres. The period of oscillation is .................

$A$ mass $m$ attached to the free end of a spring executes $SHM$ with a period of $1\; s$. If the mass is increased by $3\; kg$,the period of oscillation increases by $1\; s$. The value of mass $m$ is $..............kg$.

$A$ mass $m_1$ connected to a horizontal spring performs $S.H.M.$ with amplitude $A$. While mass $m_1$ is passing through the mean position,another mass $m_2$ is placed on it so that both the masses move together with amplitude $A_1$. The ratio of $\frac{A_1}{A}$ is:

$A$ mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period:

$A$ particle at the end of a spring executes simple harmonic motion with a period $t_1$,while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$,then

$A$ solid sphere of mass $M$ and radius $R$ is attached to a spring of negligible mass kept on a horizontal plane such that it can roll without slipping. The sphere is made to execute $SHM$ by stretching it through a distance and releasing it. The time period of such oscillation is ($K=$ spring constant).