The maximum potential energy of a block execu | vedclass

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

Question

(A) For a block executing $S.H.M.$, the total mechanical energy is constant and is equal to the maximum potential energy $E$ at the extreme position $

Vedclass · Accepted Answer

$\frac{3E}{4}$

Vedclass · Answer

(A) For a block executing $S.H.M.$, the total mechanical energy is constant and is equal to the maximum potential energy $E$ at the extreme position $(x = A)$.Total energy $E = \frac{1}{2} k A^2$.The potential energy at any displacement $x$ is given by $U = \frac{1}{2} k x^2$.At $x = A/2$, the potential energy $U$ is:$U = \frac{1}{2} k (A/2)^2 = \frac{1}{2} k (A^2/4) = \frac{1}{4} (\frac{1}{2} k A^2) = \frac{E}{4}$.The kinetic energy $K$ at any position is given by $K = E - U$.Substituting the values, $K = E - \frac{E}{4} = \frac{3E}{4}$.

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

Similar Questions

The amplitude of a particle executing $S.H.M.$ is $3 \,cm$. The displacement at which its kinetic energy will be $25 \%$ more than the potential energy is (in $\,cm$)

For a particle executing simple harmonic motion, the kinetic energy of the particle at a distance of $4 \,cm$ from the mean position is $\frac{1}{3}$ of the maximum kinetic energy. The amplitude of the motion is

The total energy of a particle executing $S.H.M.$ is $80 \, J$. What is the potential energy when the particle is at a distance of $\frac{3}{4}$ of amplitude from the mean position?

Show that for a particle in linear $SHM$,the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

$A$ particle undergoing simple harmonic motion has time-dependent displacement given by $x(t) = A \sin \left( \frac{\pi t}{90} \right)$. The ratio of kinetic energy to potential energy of the particle at $t = 210 \ s$ will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module