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Two identical pendulums oscillate with a constant phase difference $\frac{\pi}{4}$ and same amplitude. If the maximum velocity of one is $v$, the maximum velocity of the other will be ........
A particle executes linear simple harmonic motion with an ampilitude of $3\,cm$ . When the particle is at $2\,cm$ from the mean position , the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
Kinetic energy of a particle executing simple harmonic motion in straight line is $pv^2$ and potential energy is $qx^2$, where $v$ is speed at distance $x$ from the mean position. It time period is given by the expression
$Assertion :$ The time-period of pendulum, on a satellite orbiting the earth is infinity.
$Reason :$ Time-period of a pendulum is inversely proportional to $\sqrt g$
A particle is executing $SHM$ along a straight line. Its velocities at distance $x_1$ and $x_2$ from the mean position are $V_1$ and $V_2$ respectively. Its time period is
On a frictionless horizontal plane, a bob of mass $m=0.1 kg$ is attached to a spring with natural length $l_0=0.1 m$. The spring constant is $k_1=0.009 Nm ^{-1}$ when the length of the spring $I > l_0$ and is $k_2=0.016 Nm ^{-1}$ when $ I < l_0$. Initially the bob is released from $l=0.15 m$. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is $T=(n \pi) s$, then the integer closest to $n$ is. . . . .
A rod of mass $‘M’$ and length $‘2L’$ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of $‘m’$ are attached at distance $‘L/2’$ from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value of ratio $m/M$ is close to