The total energy of a body executing simple h | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The total energy $E$ of a body executing simple harmonic motion $(SHM)$ is given by $E = \frac{1}{2} m \omega^2 a^2$,where $a$ is the amplitude.At

Vedclass · Accepted Answer

$\frac{3 E}{4}$

Vedclass · Answer

(B) The total energy $E$ of a body executing simple harmonic motion $(SHM)$ is given by $E = \frac{1}{2} m \omega^2 a^2$,where $a$ is the amplitude.At any displacement $y$,the potential energy $U$ is given by $U = \frac{1}{2} m \omega^2 y^2$.The kinetic energy $K$ is the difference between total energy and potential energy: $K = E - U$.Substituting the expressions,$K = \frac{1}{2} m \omega^2 a^2 - \frac{1}{2} m \omega^2 y^2 = \frac{1}{2} m \omega^2 (a^2 - y^2)$.Given that the displacement $y = \frac{a}{2}$,we substitute this into the kinetic energy formula:$K = \frac{1}{2} m \omega^2 (a^2 - (\frac{a}{2})^2) = \frac{1}{2} m \omega^2 (a^2 - \frac{a^2}{4}) = \frac{1}{2} m \omega^2 (\frac{3a^2}{4})$.Since $E = \frac{1}{2} m \omega^2 a^2$,we can write $K = \frac{3}{4} (\frac{1}{2} m \omega^2 a^2) = \frac{3E}{4}$.

The total energy of a body executing simple harmonic motion is $E$. When the displacement is half of the amplitude,the kinetic energy is:

Similar Questions

$A$ particle is executing simple harmonic motion with a time period $T$. At time $t = 0$,it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like:

The $P.E.$ of a particle executing $SHM$ at a distance $x$ from its equilibrium position is

The equation of motion of a particle executing simple harmonic motion is given by $x=3 \sin \left(6 t+\frac{\pi}{6}\right)$,where $x$ is in metres and $t$ is in seconds. The ratio of the potential and kinetic energies of the particle at time $t=0$ is

Draw a graph to show the variation of $PE$,$KE$ and total energy of a simple harmonic oscillator with displacement.

$A$ body is executing a linear $S.H.M.$ Its potential energies at the displacements $x$ and $y$ are $E_1$ and $E_2$ respectively. Its potential energy at displacement $(x+y)$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module