In a seconds pendulum, mass of bob is $30\, gm$. If it is replaced by $90\, gm$ mass. Then its time period will .... $\sec$
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(b) Time period is independent of mass of bob of pendulum.
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Two particles are in $SHM$ in a straight line. Amplitude $A$ and time period $T$ of both the particles are equal. At time $t=0,$ one particle is at displacement $y_1= +A$ and the other at $y_2= -A/2,$ and they are approaching towards each other. After what time they cross each other ?
A load of mass $m$ falls from a height $h$ on to the scale pan hung from the spring as shown in the figure. If the spring constant is $k$ and mass of the scale pan is zero and the mass $m$ does not bounce relative to the pan, then the amplitude of vibration is
A particle executes simple harmonic motion with an amplitude of $4 \mathrm{~cm}$. At the mean position, velocity of the particle is $10 \mathrm{~cm} / \mathrm{s}$. The distance of the particle from the mean position when its speed becomes $5 \mathrm{~cm} / \mathrm{s}$ is $\sqrt{\alpha} \mathrm{cm}$, where $\alpha=$____________.
A particle performs $SHM$ about $x = 0$ such that at $t = 0$ it is at $x = 0$ and moving towards positive extreme. The time taken by it to go from $x = 0$ to $x = \frac{A}{2}$ is ..... times the time taken to go from $x = \frac{A}{2}$ to $A$. The most suitable option for the blank space is
A body executes $SHM$ under the influence of one force and has a period $T_1\, second$ and the same body executes $SHM$ with period $T_2\, second$ when under the influence of another force. When bothforces act simultaneously and in the same direction, then the time period of the same body is
The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy ${U}({x})$ versus time $({t})$ plot of the particle is correctly shown in figure:
The displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a\sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period)
A particle of mass $10\, gm$ is describing $S.H.M.$ along a straight line with period of $2\, sec$ and amplitude of $10, cm$. Its kinetic energy when it is at $5 \,cm$ from its equilibrium position is