A body performs simple harmonic oscillations | vedclass

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

Question

(C) The total energy of a body in simple harmonic motion is $E = \frac{1}{2} k A^2,$ where $A$ is the amplitude.Given that $AE = 2R$ and $C$ is the mi

Vedclass · Accepted Answer

$\sqrt{3} R$

Vedclass · Answer

(C) The total energy of a body in simple harmonic motion is $E = \frac{1}{2} k A^2,$ where $A$ is the amplitude.Given that $AE = 2R$ and $C$ is the midpoint,the amplitude $A = R$.The kinetic energy at any position $x$ is given by $K = \frac{1}{2} k (A^2 - x^2)$.According to the problem,at $B$ and $D$,the kinetic energy is one-fourth of the maximum value:$\frac{1}{2} k (A^2 - x^2) = \frac{1}{4} (\frac{1}{2} k A^2)$$A^2 - x^2 = \frac{1}{4} A^2$$x^2 = \frac{3}{4} A^2$$x = \pm \frac{\sqrt{3}}{2} A$Since $A = R$,the positions of $B$ and $D$ are $x = \pm \frac{\sqrt{3}}{2} R$.The distance between $B$ and $D$ is $|x_D - x_B| = |\frac{\sqrt{3}}{2} R - (-\frac{\sqrt{3}}{2} R)| = \sqrt{3} R$.

$A$ body performs simple harmonic oscillations along the straight line $ABCDE$ with $C$ as the midpoint of $AE.$ Its kinetic energies at $B$ and $D$ are each one-fourth of its maximum value. If $AE = 2R,$ the distance between $B$ and $D$ is

Similar Questions

$A$ particle executing a simple harmonic motion of period $2 \ s$. When it is at its extreme displacement from its mean position,it receives an additional energy equal to what it had in its mean position. Due to this,in its subsequent motion,

The maximum potential energy of a block executing $S.H.M.$ is $E$ and amplitude of oscillation is $A$. The kinetic energy of the block at amplitude $A/2$ is

When the displacement of a simple harmonic oscillator is one third of its amplitude,the ratio of total energy to the kinetic energy is $\frac{x}{8}$,where $x=$ . . . . . . .

Write the maximum velocity of a $SHM$ oscillator in terms of mechanical energy $E$ and mass of oscillator $m$.

The displacement of a simple harmonic motion of amplitude $6 \text{ cm}$ when its kinetic energy is equal to its potential energy is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module