A block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in figure. The block is displaced by $x$ towards right and released. The velocity of the block when it is at $x/2$ will be
$\sqrt {\frac{{\left( {{k_1} + {k_2}} \right){x^2}}}{{2m}}} $
$\sqrt {\frac{3}{4}\frac{{\left( {{k_1} + {k_2}} \right){x^2}}}{m}} $
$\sqrt {\frac{{\left( {{k_1} + {k_2}} \right){x^2}}}{m}} $
$\sqrt {\frac{{\left( {{k_1} + {k_2}} \right){x^2}}}{4m}} $
A weightless spring which has a force constant oscillates with frequency $n$ when a mass $m$ is suspended from it. The spring is cut into two equal halves and a mass $2m $ is suspended from it. The frequency of oscillation will now become
A block with mass $M$ is connected by a massless spring with stiffiess constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: ($i$) when the block is at $x_0$; and ($ii$) when the block is at $x=x_0+A$. In both the cases, a perticle with mass $m$ is placed on the mass $M$ ?
($A$) The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{M}{m+M}}$, whereas in the second case it remains unchanged
($B$) The final time period of oscillation in both the cases is same
($C$) The total energy decreases in both the cases
($D$) The instantaneous speed at $x_0$ of the combined masses decreases in both the cases
$A$ block of mass $M_1$ is hanged by a light spring of force constant $k$ to the top bar of a reverse Uframe of mass $M_2$ on the floor. The block is pooled down from its equilibrium position by $a$ distance $x$ and then released. Find the minimum value of $x$ such that the reverse $U$ -frame will leave the floor momentarily.
Two springs of force constants $K$ and $2K$ are connected to a mass as shown below. The frequency of oscillation of the mass is
If a spring has time period $T$, and is cut into $n$ equal parts, then the time period of each part will be