The displacements of two particles executing $S.H.M.$ on the same line are given. as $y_1=a \sin \left(\frac{\pi}{2} t+\phi\right)$ and $y_2=b \sin \left(\frac{2 \pi}{3} t+\phi\right)$. The phase difference between them at $t=1 \,s$ is .........
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(d)
Phase difference between them is just difference in the angular values.
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A tunnel is dug in the earth across one of its diameter. Two masses $‘m’\,\& \,‘2m’$ are dropped from the ends of the tunnel. The masses collide and stick to each other and perform $S.H.M.$ Then amplitude of $S.H.M.$ will be : [$R =$ radius of the earth]
Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be
A mass $m$ is suspended from a spring of force constant $k$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is
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A spring is stretched by $0.20\, m$, when a mass of $0.50\, kg$ is suspended. When a mass of $0.25\, kg$ is suspended, then its period of oscillation will be .... $\sec$ $(g = 10\,m/{s^2})$
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 particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is