An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross$-$section, $A$. 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
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The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended , the period of oscillation will now be
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 particle performing $SHM$ is found at its equilibrium at $t = 1\,sec$. and it is found to have a speed of $0.25\,m/s$ at $t = 2\,sec$. If the period of oscillation is $6\,sec$. Calculate amplitude of oscillation
Infinite springs with force constant $k$, $2k$, $4k$ and $8k$.... respectively are connected in series. The effective force constant of the spring will be
The amplitude and the periodic time of a $S.H.M.$ are $ 5\,cm$ and $6\,sec$ respectively. At a distance of $2.5\,cm$ away from the mean position, the phase will be
A simple harmonic oscillator of angular frequency $2\,rad\,s^{-1}$ is acted upon by an external force $F = sin\,t\,N .$ If the oscillator is at rest in its equilibrium position at $t = 0,$ its position at later times is proportional to