The displacements of two particles of same ma | vedclass

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

Question

(D) The energy of a particle executing $SHM$ is given by $E = \frac{1}{2} m \omega^2 A^2$, where $m$ is the mass, $\omega$ is the angular frequency, a

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(D) The energy of a particle executing $SHM$ is given by $E = \frac{1}{2} m \omega^2 A^2$, where $m$ is the mass, $\omega$ is the angular frequency, and $A$ is the amplitude.For the first particle, $x_1 = 4 \sin (10t + \frac{\pi}{6})$, the amplitude $A_1 = 4$ and angular frequency $\omega_1 = 10$.The energy is $E_1 = \frac{1}{2} m (10)^2 (4)^2 = \frac{1}{2} m (100)(16) = 800m$.For the second particle, $x_2 = 5 \cos (\omega t)$, the amplitude $A_2 = 5$ and angular frequency is $\omega$.The energy is $E_2 = \frac{1}{2} m \omega^2 (5)^2 = \frac{25}{2} m \omega^2$.Given that the energies are equal, $E_1 = E_2$.$800m = \frac{25}{2} m \omega^2$.$1600 = 25 \omega^2$.$\omega^2 = \frac{1600}{25} = 64$.$\omega = 8 	ext{ unit}$.

Column-$I$	Column-$II$
$(a)$ $K = 10\,J$	$(i)$ $U = 40\,J$
$(b)$ $K = 60\,J$	$(ii)$ $U = 90\,J$
	$(iii)$ $U = 50\,J$

The displacements of two particles of same mass executing $SHM$ are represented by the equations $x_1=4 \sin \left(10 t+\frac{\pi}{6}\right)$ and $x_2=5 \cos (\omega t)$. The value of $\omega$ for which the energies of both the particles remain same is (in $\text{ unit}$)

Similar Questions

Assertion $(A)$: In $S.H.M$,kinetic and potential energy become equal when the distance is $1/\sqrt{2}$ times its amplitude. Reason $(R)$: The potential energy of a particle executing $S.H.M$ is periodic with time period being maximum at the extreme displacement.

The frequency at which kinetic energy changes into potential energy in a simple harmonic motion ($S$.$H$.$M$.) with frequency $f$ is:

$A$ linear harmonic oscillator of force constant $2 \times 10^6 \, N/m$ and amplitude $0.01 \, m$ has a total mechanical energy of $160 \, J$. Its

At what position in simple harmonic motion are the kinetic energy and potential energy equal?

Vedclass Test Series

Exam Paper Generator

Online Exam Module