A particle starts simple harmonic motion from the mean position. Its amplitude is $a$ and total energy $E$. At one instant its kinetic energy is $3E/4.$ Its displacement at that instant is
JEE MAIN 2021, Medium
Download our app for free and get started
(b) $\frac{K}{E} = \frac{{\frac{1}{2}m{\omega ^2}({a^2} - {y^2})}}{{\frac{1}{2}m{\omega ^2}{a^2}}}$
$= \frac{{{a^2} - {y^2}}}{{{a^2}}} $
$= 1 - \frac{{{y^2}}}{{{a^2}}}$
So, $\frac{{\left( {\frac{{3E}}{4}} \right)}}{E} = 1 - \frac{{{y^2}}}{{{a^2}}}$
$\Rightarrow \frac{{{y^2}}}{{{a^2}}} = 1 - \frac{3}{4} = \frac{1}{4}$
$ \Rightarrow y = \frac{a}{2}$.
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
- 1Starting from the origin a body oscillates simple harmonically with a period of $2\ s$. After what time will its kinetic energy be $75\%$ of the total energy?View Solution
- 2View SolutionThe effective spring constant of two spring system as shown in figure will be
- 3Time period of a simple pendulum is $T$. The angular displacement for amplitude is $\beta$. How much time the bob of pendulum will take to move from equilibrium position $O$ to $A$, making an angle $\alpha$ at the supportView Solution
- 4For a particle showing motion under the force $F=-5(x-2)$, the motion is ...........View Solution
- 5A pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels same distance per unit time, the period of oscillation isView Solution
- 6Function $x$ = $A sin^2 wt + B cos^2 wt + C sin wt \ cos wt$ does not represents $SHM$ for this conditionView Solution
- 7The displacement of a particle executing $S.H.M.$ is given by $x=0.01 \sin 100 \pi(t+0.05)$. The time period is ........ $s$View Solution
- 8The potential energy of a particle of mass $100 \,g$ moving along $x$-axis is given by $U=5 x(x-4)$, where $x$ is in metre. The period of oscillation is .................View Solution
- 9The displacement of an oscillator is given by $x = a\, \sin \, \omega t + b\, \cos \, \omega t$. where $a, b$ and $\omega$ are constant. Then :-View Solution
- 10The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height h above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\, sec$, the tension in the string when the bob passes through $O$ isView Solution
