A simple harmonic oscillator has a period of $0.01 \,sec$ and an amplitude of $0.2\, m$. The magnitude of the velocity in $m{\sec ^{ - 1}}$ at the centre of oscillation is
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A body executes sample harmonic motion under the action of a force $F_1$ with a time period $(4 / 5)\ sec$. If the force is changed to $F_ 2$ it executes $SHM$ with time period $(3 / 5)\ sec$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body, it's time period (in $second$) is
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 mass m performs oscillations of period $T$ when hanged by spring of force constant $K$. If spring is cut in two parts and arranged in parallel and same mass is oscillated by them, then the new time period will be
A particle performs simple harmonic motion with a period of $2$ second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{ a } s .$ The value of $'a'$ to the nearest integer is.........
The height of liquid column in a $U$ tube is $0.3$ meter. If the liquid in one of the limbs is depressed and then released, then the time period of liquid column will be $.......\,sec$
The metallic bob of simple pendulum has the relative density $5$. The time period of this pendulum is $10\,s$. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt{ x } s$. The value of $x$ will be.
A block of mass $0.1\, kg$ is connected to an elastic spring of spring constant $640\, Nm^{-1}$ and oscillates in a damping medium of damping constant $10^{-2}\, kg\,s^{-1}$ . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to ..... $s$
A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ${\omega _0}$ - An external force $F (t)$ proportional to $\cos \omega \,t((\omega \ne {\omega _0})$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
A system of two identical rods ($L-$ shaped) of mass $m$ and length $l$ are resting on a peg $P$ as shown in the figure. If the system is displaced in its plane by a small angle $\theta ,$ find the period of oscillations :