On a smooth inclined plane,a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has a force constant $K$,the period of oscillation of the body (assuming the springs are massless) is

$A$ mass of $200 \text{ g}$ is suspended from a spring with a force constant of $80 \text{ N/m}$. What is the time period of the oscillation in seconds?

$A$ light spring is suspended with mass $m_1$ at its lower end and its upper end fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is $T$ seconds. When a mass $m_2$ is added to $m_1$ and the system is made to oscillate,the period is found to be $\frac{3}{2} T$. The ratio $m_1 : m_2$ is

An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15 \,cm/s$ and the period is $628 \,ms$. The amplitude of the motion in $cm$ is:

$A$ spring-mass system (mass $m$,spring constant $k$,and natural length $\ell_{0}$) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the center of the disc. If the disc,together with the spring-mass system,rotates about its axis with an angular velocity $\omega$ (where $k >> m \omega^{2}$),the relative change in the length of the spring is best given by which option?

The upper end of the spring is fixed and a mass $m$ is attached to its lower end. When the mass is slightly pulled down and released,it oscillates with a time period of $3 \text{ s}$. If the mass $m$ is increased by $1 \text{ kg}$,the time period becomes $5 \text{ s}$. The value of $m$ is (mass of the spring is negligible).