A particle of mass $m$ is moving along a trajectory given by
$x = x_0 + a\, cos\,\omega_1 t$
$y = y_0 + b\, sin\,\omega_2t$
The torque, acing on the particle about the origin, at $t = 0$ is
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In the figure, ${S_1}$ and ${S_2}$ are identical springs. The oscillation frequency of the mass $m$ is $f$. If one spring is removed, the frequency will become
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor, the velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$
A block of mass $m$ is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring, then the maximum amplitude of motion so that both the block will remain in contact is
The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\ N/m.$ The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\ kg$ and $m_2 = 27 \,kg \,?$
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
A particle of mass $m$ executes simple harmonic motion with amplitude $a$ and frequency $v$. The average kinetic energy during its motion from the position of equilibrium to the end is
Find maximum amplitude for safe $SHM$ (block does not topple during $SHM$) of $a$ cubical block of side $'a'$ on a smooth horizontal floor as shown in figure (spring is massless)
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
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 ........