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A body is executing Simple Harmonic Motion. At a displacement $x$ its potential energy is ${E_1}$ and at a displacement y its potential energy is ${E_2}$. The potential energy $E$ at displacement $(x + y)$ is
A particle executes simple hormonic motion between $x =\, -A$ and $x = +A$ . It starts from $x = 0$ moves in $+x-$ direction. The time taken for it to move from $x = 0$ to $x = \frac {A}{2}$ is $T_1$ and to move from $\frac {A}{2}$ to $\frac {A}{\sqrt 2}$ is $T_2$ , then
The velocity vector $v$ and displacement vector $x$ of a particle executing SHM are related as $\frac{v d v}{d x}=-\omega^2 x$ with the initial condition $v=v_0$ at $x=0$. The velocity $v$, when displacement is $x$, is
The period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$, is given by
Time period of a simple pendulum in a stationary lift is ' $T$ '. If the lift accelerates with $\frac{ g }{6}$ vertically upwards then the time period will be .....
A simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure below. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?
The potential energy of a particle of mass $1\, kg$ in motion along the $x-$ axis is given by $U = 4\,(1 -cos\,2x)$, where $x$ is in $metres$ . The period of small oscillation (in $second$ ) is
The piston in the cylinder head of locomotive has a stroke of $6\,m$ (which is twice the amplitude). If the piston executing simple harmonic motion with an angular frequency of $200\, rad\, min^{-1}$, its maximum speed is .... $ms^{-1}$
A particle is executing Simple Harmonic Motion $(SHM)$. The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be