In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
JEE MAIN 2021, Medium
Download our app for free and get started
$K =\frac{1}{2} m \omega^{2}\left( A ^{2}- x ^{2}\right)$
$=\frac{1}{2} m \omega^{2}\left( A ^{2}-\frac{ A ^{2}}{4}\right)$
$=\frac{1}{2} m \omega^{2}\left(\frac{3 A ^{2}}{4}\right)$
$K =\frac{3}{4}\left(\frac{1}{2} m \omega^{2} A ^{2}\right)$
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
- 1What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $10\,cm$ ($g = 9.8\, m/s^2$) ..... $m/s$View Solution
- 2A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; $x = {a_1}\,\cos \,\omega t$ and $y = {a_2}\,\cos \,2\,\omega t$ traces a curve given byView Solution
- 3The mass of a particle is $1\,\,kg$ and it is moving along $x-$ axis. The period of its small oscillation is $\frac {\pi }{2}$ . Its potential energy may beView Solution
- 4Due to some force $F_1$ a body oscillates with period $4/5\, sec$ and due to other force $F_2$ oscillates with period $3/5\, sec$. If both forces act simultaneously, the new period will be .... $\sec$View Solution
- 5When a particle executes $SHM$ the nature of graphical representation of velocity as a function of displacement is :View Solution
- 6The equation of motion of a particle is $\frac{{{d^2}y}}{{d{t^2}}} + Ky = 0$, where $K$ is positive constant. The time period of the motion is given byView Solution
- 7Match $List - I$ with $List - II$View Solution
Choose the correct answer from the options given below
- 8Initially system is in equilibrium. Time period of $SHM$ of block in vertical direction isView Solution
- 9A simple pendulum with a metallic bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $1 / 4$ that of metal, the time period of the same pendulum will be ...........View Solution
- 10A mass $M$ is suspended by two springs of force constants $K_1$ and $K_2$ respectively as shown in the diagram. The total elongation (stretch) of the two springs isView Solution
