A circular arc of mass $m$ is connected with the help of two massless strings as shown in the figuw in vertical plane. About point $P$, small oscillations are given in the plane of the arc. Time period of the oscillations of $SHM$ will be
Diffcult
Download our app for free and get started
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
The displacement of a particle varies according to the relation $x$ = $3 sin100t + 8cos^2 50t$. Which of the following is $INCORRECT$ about this motion
On the superposition of two harmonic oscillations represented by ${x_1} = a\,\sin \,\left( {\omega t + {\phi _1}} \right)$ and ${x_2} = a\,\sin \,\left( {\omega t + {\phi _2}} \right)$ a resulting oscillation with the same time period and amplitude is obtained. The value of ${\phi _1} - {\phi _2}$ is .... $^o$
A particle starts oscillating simple harmonically from its equilibrium position then, the ratio of kinetic energy and potential energy of the particle at the time $T/12$ is : ($T =$ time period)
A particle of mass m is executing oscillations about the origin on the $X-$axis. Its potential energy is $U(x) = k{[x]^3}$, where $k$ is a positive constant. If the amplitude of oscillation is $a$, then its time period $T$ is
A weightless spring of length $60\, cm$ and force constant $200\, N/m$ is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of $0.25\, kg$ is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is
A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of time period $T$. If the mass is increased by m, the time period becomes $5T/3$. Then the ratio of $m/M$ is
A massless spring $(k = 800\, N/m)$, attached with a mass $(500\, g)$ is completely immersed in $1\, kg$ of water. The spring is stretched by $2\, cm$ and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass $= 400\, J/kg\, K$, specific heat of water $= 4184\, J/kg\, K$)
A particle executes simple harmonic motion represented by displacement function as $x(t)=A \sin (\omega t+\phi)$
If the position and velocity of the particle at $t=0\, {s}$ are $2\, {cm}$ and $2\, \omega \,{cm} \,{s}^{-1}$ respectively, then its amplitude is $x \sqrt{2} \,{cm}$ where the value of $x$ is ..... .