A body is executing simple harmonic motion with an angular frequency $2\,rad/s$. The velocity of the body at $20\, mm$ displacement, when the amplitude of motion is $60\, mm$, is ...... $mm/s$
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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
A rod of mass $m$ and length $l$ is suspended from ceiling with two string of length $l$ as shown. When the rod is given a small push in the plane of page and released time period is $T_1$ and when the rod is given a push perpendicular to plane time period of oscillation is $T_2$ . The ratio $\frac{{T_1^2}}{{T_2^2}}$ is
The plot of velocity $(v)$ versus displacement $(x)$ of a particle executing simple harmonic motion is shown in figure. The time period of oscillation of particle is .........
A clock which keeps correct time at ${20^o}C$, is subjected to ${40^o}C$. If coefficient of linear expansion of the pendulum is $12 \times {10^{ - 6}}/^\circ C$. How much will it gain or loose in time
The displacement of an object attached to a spring and executing simple harmonic motion is given by $ x= 2 \times 10^{-9}$ $ cos$ $\;\pi t\left( m \right)$ .The time at which the maximum speed first occurs is
A simple pendulum is made of a body which is a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of pendulum will
The displacement of a particle executing periodic motion is given by :
$y = 4cos^2\,(t/2)sin\,(1000t)$
This expression may be considered to be a result of superposition of
$A$ particle of mass m is constrained to move on $x$ -axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example, when the particle is to the left of $E, F$ points to the right. The magnitude of $F$ is a constant $F$ except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards left from the equilibrium position $E$ and released from rest at $t = 0.$ Find minimum time it will take to reach from $x = - \frac{A}{2}$ to $0$.
The variation of kinetic energy $(KE)$ of a particle executing simple harmonic motion with the displacement $(x)$ starting from mean position to extreme position $(A)$ is given by