A particle of mass 5 x 10^-5 kg is placed at the lowest point of a smooth parabola having the equation x² = 40y (x, y in cm). If it is displaced slightly and it moves such that it is constrained to move along the parabola, the angular frequency of oscillation will be, approximately

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36 \mathrm{m}$ and covers $30°$ in $0.1 \mathrm{s}$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoration force per unit mass when $P$ touches $M$ will be :

A tray of mass $12 \mathrm{kg}$ is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of $1.5 \mathrm{s}$. The spring constant of each spring is

A cone with half the density of water is floating in water as shown in figure. It is depressed down by a small distance $\delta \left(\ll \mathrm{H}\right)$ and released. The frequency of simple harmonic oscillations of the cone is

A particle of mass $1 \mathrm{mg}$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $2 \mathrm{m}$ when each is carrying same charge $q$. If the free charged particle is displaced from its equilibrium position through distance $x$ $\left(x<<1 \mathrm{m}\right)$. The particle executes SHM. Its angular frequency of oscillation will be _______ $\times {10}^5 \mathrm{rad} {\mathrm{s}}^{-1}$ (if $q^2=10C^2$)

A particle of mass $m$ is attached to four springs with spring constant $k,k,2k$ and $2k$ as shown in the figure. Four springs are attached to the four corners of a square and a particle is placed at the center. If the particle is pushed slightly towards any side of the square and released, the period of oscillation will be

In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k.$ The mass oscillates on a frictionless surface with time period $T$ and amplitude $A.$ When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be: