A body is executing simple harmonic motion. A | vedclass

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

Question

(B) For a body executing $SHM$,the potential energy $U$ at displacement $d$ is given by $U = \frac{1}{2} k d^2$. Given: $E_1 = \frac{1}{2} k x^2 \impl

Vedclass · Accepted Answer

$\sqrt{E}=\sqrt{E_1}+\sqrt{E_2}$

Vedclass · Answer

(B) For a body executing $SHM$,the potential energy $U$ at displacement $d$ is given by $U = \frac{1}{2} k d^2$. Given: $E_1 = \frac{1}{2} k x^2 \implies x = \sqrt{\frac{2 E_1}{k}}$ $E_2 = \frac{1}{2} k y^2 \implies y = \sqrt{\frac{2 E_2}{k}}$ The potential energy $E$ at displacement $(x+y)$ is: $E = \frac{1}{2} k (x+y)^2$ $E = \frac{1}{2} k (x^2 + y^2 + 2xy)$ $E = \frac{1}{2} k x^2 + \frac{1}{2} k y^2 + 2 \left( \frac{1}{2} k x y \right)$ $E = E_1 + E_2 + 2 \sqrt{\left( \frac{1}{2} k x^2 \right) \left( \frac{1}{2} k y^2 \right)}$ $E = E_1 + E_2 + 2 \sqrt{E_1 E_2}$ $E = (\sqrt{E_1} + \sqrt{E_2})^2$ Taking the square root on both sides: $\sqrt{E} = \sqrt{E_1} + \sqrt{E_2}$

$A$ body is executing simple harmonic motion. At a displacement $x$,its potential energy is $E_1$ and at a displacement $y$,its potential energy is $E_2$. The potential energy $E$ at a displacement $(x+y)$ is

Similar Questions

The potential energy of a simple harmonic oscillator,when the particle is halfway to its endpoint,is

$A$ bob of a simple pendulum of mass $m$ performs $SHM$ with amplitude $A$ and period $T$. The kinetic energy of the pendulum at displacement $x = \frac{A}{2}$ will be:

$A$ linear harmonic oscillator of force constant $2 \times 10^6\,N/m$ and amplitude $0.01\,m$ has a total mechanical energy of $160\,J$. Which of the following statements is correct?

$A$ particle is executing simple harmonic motion with a time period of $3 \,s$. At a position where the displacement of the particle is $60 \%$ of its amplitude, the ratio of the kinetic and potential energies of the particle is

The potential energy of a particle with displacement $X$ is $U(X)$. The motion is simple harmonic,when ($K$ is a positive constant)

Vedclass Test Series

Exam Paper Generator

Online Exam Module