A massless spring $(k = 800\, N/m)$, attached with a mass $(500\, g)$ is completely immersed in $1\, kg$ of water. The spring is stretched by $2\, cm$ and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass $= 400\, J/kg\, K$, specific heat of water $= 4184\, J/kg\, K$)
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At time $t = 0$, a simple harmonic oscillator is at its extreme position. If it covers half of the amplitude distance in $1\, second$, then the time period of oscillation is ..... $s$
A mass $m$ is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are $k_1$ and $k_2$ respectively. When set into vertical vibrations, the period will be
silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12} /sec$. What is the force constant of the bonds connecting one atom with the other? ................ $\mathrm{N/m}$ (Mole wt. of silver $= 108 $ andAvagadro number $= 6.02 \times 10^{23}$ $gm \ mole^{ -1}$ )
In the figure shown, there is friction between the blocks $P$ and $Q$ but the contact between the block $Q$ and lower surface is frictionless. Initially the block $Q$ with block $P$ over it lies at $x=0$, with spring at its natural length. The block $Q$ is pulled to right and then released. As the spring - blocks system undergoes $S.H.M.$ with amplitude $A$, the block $P$ tends to slip over $Q . P$ is more likely to slip at
In an engine the piston undergoes vertical simple harmonic motion with amplitude $7\, cm$ . A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to ...... $Hz$
A particle executes $S.H.M.$ of amplitude A along $x$-axis. At $t =0$, the position of the particle is $x=\frac{A}{2}$ and it moves along positive $x$-axis the displacement of particle in time $t$ is $x=A \sin (\omega t+\delta)$, then the value $\delta$ will be