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The periodic time of a body executing simple harmonic motion is $3\, sec$. After how much interval from time $t = 0$, its displacement will be half of its amplitude ..... $\sec$
Two pendulum have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum they will be again in the same phase
Block $A$ is hanging from a vertical spring and it is at rest. Block $'B'$ strikes the block $'A'$ with velocity $v$ and stick to it. Then the velocity $v$ for which the spring just attains natural length is:
A ball is rolling without slipping in a spherical shallow bowl (radius $R$ ) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled, then the time period of oscillation
A loaded vertical spring executes $S.H.M.$ with a time period of $4\; sec$. The difference between the kinetic energy and potential energy of this system varies with a period of ........$sec$
A particle of mass m is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k{[x]^3}$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then its time period $T$ is
A mass $M$, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\frac{{{A_1}}}{{{A_2}}}$ is