The total energy of the body executing $S.H.M.$ is $E$. Then the kinetic energy when the displacement is half of the amplitude, is
Medium
Download our app for free and get started
(c) Total energy in $SHM $ $E = \frac{1}{2}m{\omega ^2}{a^2}$; (where $a =$ amplitude)
Potential energy $U = \frac{1}{2}m{\omega ^2}({a^2} - {y^2}) $
$= E - \frac{1}{2}m{\omega ^2}{y^2}$
When $y = \frac{a}{2}$
$⇒$ $U = E - \frac{1}{2}m{\omega ^2}\left( {\frac{{{a^2}}}{4}} \right)$
$= E - \frac{E}{4} = \frac{{3E}}{4}$
Download our appand 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.*
Similar Questions
- 1A simple perdulum performs simple harmonic motion about $x=0$ with an amplitude $a$ and time period $T$. The speed of the pendulum at $x=a/2$ will beView Solution
- 2A particle executes $SHM $ in a line $4\, cm $ long. Its velocity when passing through the centre of line is $12\, cm/s$. The period will be ..... $s$View Solution
- 3A body is performing simple harmonic motion with amplitude a and time period $T$. Variation of its acceleration $(f)$ with time $(t)$ is shown in figure. If at time $t$, velocity of the body is $v$, which of the following graphs is correctView Solution
- 4Two parallel discs are connected by a rigid rod of length $L=0.5 \,m$ centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms are incident on one of the discs axially at different velocities $v$, while the system is rotated at angular speed of $600 \,rev / second$, so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in metre/second) of the atoms that will emerge at the other end.View Solution
- 5Two simple pendulums of lengths $1.44 \,m$ and $1\, m$ start swinging together. After how many vibrations will they again start swinging togetherView Solution
- 6The motion of a particle as per $x=Asin \omega t + Bcos\omega t$ is :-View Solution
- 7The displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a\sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period)View Solution
- 8A plank with a small block on top of it is under going vertical $SHM.$ Its period is $2\, sec.$ The minimum amplitude at which the block will separate from plank is :View Solution
- 9View SolutionIdentify the correct statement
- 10In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_{1}$ of the force, while the energy is maximum for a frequency $\omega_{2}$ of the force, thenView Solution