Physics Oscillations

When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y(t) = y₀sin² ωt, where ' y ' is measured from the lower end of unstretched spring. Then ω is:

A block of mass $m$  attached to a 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 wire of density 9 * 10⁻³ kg cm⁻³ is stretched between two clamps 1 m apart. The resulting  strain in the wire is 4.9 * 10⁻⁴. The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire Y = 9 * 10¹⁰ Nm⁻²), (to the nearest integer), is

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 * 10⁻⁴. The mass of the particle is close to:

An object of mass m is suspended at the end of a massless wire of length L and area of cross-selection, A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:

A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T?, and, T (ii) back and forth in a direction perpendicular to its plane, with a period T?. The ratio T?/T? will be: