What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless ?
$\frac{\pi }{2}\sqrt {\frac{m}{k}} $
$\frac{\pi }{2}\sqrt {\frac{m}{{2k}}} $
$\frac{\pi }{2}\sqrt {\frac{{2m}}{k}} $
$\pi \sqrt {\frac{m}{{2k}}} $
In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become
A $1\,kg$ mass is attached to a spring of force constant $600\,N / m$ and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of $0.5\,kg$ slides along the surface towards the first at $3\,m / s$. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.
A body of mass $5\; kg$ hangs from a spring and oscillates with a time period of $2\pi $ seconds. If the ball is removed, the length of the spring will decrease by
What is condition for a body suspended at the end of a spring having simple harmonic oscillation ?
A mass $m =100\, gms$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16$ metre and time period equal to $2 \,sec$. Initially the mass is released from rest at $t = 0$ and displacement $x = - 0.16$ metre. The expression for the displacement of the mass at any time $t$ is