A bar of mass $m$ is suspended horizontally on two vertical springs of spring constant $k$ and $3k$ . The bar bounces up and down while remaining horizontal. Find the time period of oscillation of the bar (Neglect mass of springs and friction everywhere).
$2\pi \sqrt {\frac{m}{k}} $
$2\pi \sqrt {\frac{m}{{3k}}} $
$\pi \sqrt {\frac{{2m}}{{3k}}} $
$2\pi \sqrt {\frac{{m}}{{4k}}} $
A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be
Two masses $m_1$ and $m_2$ are suspended together by a massless spring of constant $K$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system. The amplitude of oscillations is
Find maximum amplitude for safe $SHM$ (block does not topple during $SHM$) of $a$ cubical block of side $'a'$ on a smooth horizontal floor as shown in figure (spring is massless)
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
Two springs with negligible masses and force constant of $K_1 = 200\, Nm^{-1}$ and $K_2 = 160\, Nm^{-1}$ are attached to the block of mass $m = 10\, kg$ as shown in the figure. Initially the block is at rest, at the equilibrium position in which both springs are neither stretched nor compressed. At time $t = 0,$ a sharp impulse of $50\, Ns$ is given to the block with a hammer.