The potential energy of a particle with displ | vedclass

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

Question

(A) For a particle to undergo simple harmonic motion $(SHM)$,the restoring force must be proportional to the displacement and directed towards the equ

Vedclass · Accepted Answer

$U = \frac{1}{2}KX^2$

Vedclass · Answer

(A) For a particle to undergo simple harmonic motion $(SHM)$,the restoring force must be proportional to the displacement and directed towards the equilibrium position,given by $F = -KX$,where $K$ is the force constant.The potential energy $U(X)$ is related to the force by the relation $F = -\frac{dU}{dX}$.Integrating this expression,we get $U(X) = -\int F dX = -\int (-KX) dX = \int KX dX$.Thus,$U(X) = \frac{1}{2}KX^2 + C$. Setting the potential energy at the equilibrium position $(X=0)$ to zero,we get $C = 0$.Therefore,the potential energy for simple harmonic motion is $U = \frac{1}{2}KX^2$.

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

Similar Questions

$A$ body executes simple harmonic motion with an amplitude $A$. At what displacement,from the mean position,is the potential energy of the body one fourth of its total energy?

For a particle executing $S.H.M.$,the potential energy $V$ versus displacement $x$ graph is given. The value of the restoring force constant is ..... $N/m$.

If the amplitude of a body executing $SHM$ is doubled,what will be its energy?

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

Write the expression of kinetic energy and potential energy of $SHM$ particle $(i)$ as a function of displacement $(ii)$ as a function of time.

Vedclass Test Series

Exam Paper Generator

Online Exam Module