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Two particles $P$ and $Q$ describe $SHM$ of same amplitude $a$ , frequency $v$ along the same straight line. The maximum distance between the two particles is $a \sqrt 2$ . The initial phase difference between the particles is
A particle moves such that its acceleration $a$ is given by $a = - bx$, where $x$ is the displacement from equilibrium position and b is a constant. The period of oscillation is
The particle executing $SHM$ of amplitude $'a'$ has displacement $-\frac {a}{2}$ at $t = \frac {T}{4}$ and a positive velocity. Find the initial phase of particle
A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will
A particle executes simple harmonic motion represented by displacement function as $x(t)=A \sin (\omega t+\phi)$
If the position and velocity of the particle at $t=0\, {s}$ are $2\, {cm}$ and $2\, \omega \,{cm} \,{s}^{-1}$ respectively, then its amplitude is $x \sqrt{2} \,{cm}$ where the value of $x$ is ..... .
A block of rectangular size of mass $m$ and area of cross-section $A$, floats in a liquid of density $\rho$. If we give a small vertical displacement from equilibrium, it undergoes $S H M$ with time period $T$, then
A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta)$ of thread deflection in the extreme position will be :
A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be