A particle is performing S.H.M. with energy o | vedclass

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

Question

(A) The total energy of a particle performing $S.H.M.$ is given by $E = \frac{1}{2} k A^2$,where $k = m \omega^2$.Given $E_1 = 90 \,J$ and $A_1 = 6 \,

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) The total energy of a particle performing $S.H.M.$ is given by $E = \frac{1}{2} k A^2$,where $k = m \omega^2$.Given $E_1 = 90 \,J$ and $A_1 = 6 \,cm = 0.06 \,m$.$90 = \frac{1}{2} k (0.06)^2 \implies k = \frac{180}{0.0036} = 50000 \,N/m$.When the particle is at $x = 4 \,cm = 0.04 \,m$,it is stopped. At this point,its velocity becomes zero,so the new amplitude $A_2$ of the motion becomes the displacement at that instant,i.e.,$A_2 = 4 \,cm = 0.04 \,m$.The new energy of vibration $E_2$ is given by $E_2 = \frac{1}{2} k A_2^2$.$E_2 = \frac{1}{2} 	imes 50000 	imes (0.04)^2$.$E_2 = 25000 	imes 0.0016 = 40 \,J$.

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

$A$ particle is performing $S.H.M.$ with energy of vibration $90 \,J$ and amplitude $6 \,cm$. When the particle reaches a distance of $4 \,cm$ from the mean position,it is stopped for a moment and then released. The new energy of vibration will be ........... $J$.

Similar Questions

$A$ body is executing $S$.$H$.$M$. Its potential energy is '$P_1$' and '$P_2$' at displacements '$x$' and '$y$' respectively. The potential energy at displacement $(x+y)$ is

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 $\text{ unit}$)

The mass of a particle is $1 \ kg$ and it is moving along the $x$-axis. The period of its oscillation is $\frac{\pi}{2} \ s$. Its potential energy at a displacement of $0.2 \ m$ is (in $J$)

For a particle executing $S.H.M.$,its potential energy is $8$ times its kinetic energy at a certain displacement $x$ from the mean position. If $A$ is the amplitude of $S.H.M.$,the value of $x$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module