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A $ U$ tube of uniform bore of cross-sectional area $A$ has been set up vertically with open ends facing up. Now $m$ gm of a liquid of density $d$ is poured into it. The column of liquid in this tube will oscillate with a period $T$ such that
A particle of mass $0.50 \mathrm{~kg}$ executes simple harmonic motion under force $\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}$. The time period of oscillation is $\frac{x}{35} s$. The value of $x$ is . . . . .(Given $\pi=\frac{22}{7}$ )
If the particle repeats its motion after a fixed time interval of $8 \,s$ then after how much time its maximum value of $PE$ will be attained after attaining its minimum value is ........... $s$
The equation of a particle executing simple harmonic motion is given by $x =\sin \pi\left( t +\frac{1}{3}\right) m$. At $t =1 \,s$, the speed of particle will be .......... $cm s ^{-1}$ (Given : $\pi=3.14$ )
A rectangular block of mass $5\,kg$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1\,m$ and time period $3.14\,s$. The maximum force exerted by spring on block is $.......N$.
You are holding a shallow circular container of radius $R$, filled with water to a height $h ( h < < R )$. When yon walk with speed $v$, it is seen that water starts spilling over. This happens due to the resonance of the periodic impulse given to the container (due to walking) with the oscillation of the water in the container. If the time period of water oscillating in the container is inversely proportional to $\sqrt{ h }$, then $v$ is proportional to
The motion of a mass on a spring, with spring constant ${K}$ is as shown in figure. The equation of motion is given by $x(t)= A sin \omega t+ Bcos\omega t$ with $\omega=\sqrt{\frac{K}{m}}$ Suppose that at time $t=0$, the position of mass is $x(0)$ and velocity $v(0)$, then its displacement can also be represented as $x(t)=C \cos (\omega t-\phi)$, where $C$ and $\phi$ are