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A vertical mass-spring system executes simple harmonic oscillations with a period of $2\,s$. A quantity of this system which exhibits simple harmonic variation with a period of $1\, s$ is
Two springs of force constants $300\, N / m$ (Spring $A$) and $400$ $N / m$ (Spring $B$ ) are joined together in series. The combination is compressed by $8.75\, cm .$ The ratio of energy stored in $A$ and $B$ is $\frac{E_{A}}{E_{B}} .$ Then $\frac{E_{A}}{E_{B}}$ is equal to
The motion of a particle executing $S.H.M.$ is given by $x = 0.01\sin 100\pi (t + .05)$, where $x$ is in metres and time is in seconds. The time period is ..... $\sec$
A $15 \,g$ ball is shot from a spring gun whose spring has a force constant of $600 \,N/m$. The spring is compressed by $5 \,cm$. The greatest possible horizontal range of the ball for this compression is .... $m$ ($g = 10 \,m/s^2$)
A body of mass $1\,kg$ is executing simple harmonic motion. Its displacement $y(cm)$ at $t$ seconds is given by $y = 6\sin (100t + \pi /4)$. Its maximum kinetic energy is ..... $J$