The force-deformation equation for a nonlinear spring fixed at one end is $F =4x^{1/ 2}$ , where $F$ is the force (expressed in newtons) applied at the other end and $x$ is the deformation expressed in meters
This spring mass system execute $SHM$ .
The deformation $x_0$ if a $100\ g$ block is suspended from the spring and is at rest is $0.625\ m$ .
Assuming that the slope of the force deformation curve at the point corresponding to the deformation $x_0$ can be used as an equivalent spring constant, then the frequency of vibration of the block is $\frac{{4\sqrt 5 }}{{2\pi }}$ .
None of these
Let $T_1$ and $T_2$ be the time periods of two springs $A$ and $B$ when a mass $m$ is suspended from them separately. Now both the springs are connected in parallel and same mass $m$ is suspended with them. Now let $T$ be the time period in this position. Then
Two springs of force constant $K$ and $2K$ are connected to a mass as shown below. The frequency of oscillation of the mass 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 block of mass $m$ attached to massless spring is performing oscillatory motion of amplitude $'A'$ on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $fA.$ The value of $f$ is
A uniform stick of mass $M$ and length $L$ is pivoted at its centre. Its ends are tied to two springs each of force constant $K$ . In the position shown in figure, the strings are in their natural length. When the stick is displaced through a small angle $\theta $ and released. The stick