The displacement of a particle is given by. x=A cosωt. Which of the following graph represents v

step 1 Hello and welcome to this video solution of numed. So we are given the displacement of a particl

The displacement of a particle is given by. x=A cosωt. Which...

The displacement of a particle is given by. $\mathrm{x}=\mathrm{A} \cos \omega \mathrm{t}$. Which of the following graph represents variation in potential energy as a function of time $t$ and displacement $\mathrm{x}$.
(A) I,III
(B) II,IV
(C) II,III
(D) I,IV

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Key Concepts

Graphical Representation of SHM Variables

Graphically analyzing SHM involves plotting relationships such as displacement versus time or potential energy versus displacement/time. Understanding these graphs requires recognizing the sinusoidal nature of the displacement and the quadratic dependence of potential energy on displacement, leading to curves that represent energy variations over time or with respect to the position of the oscillating particle.

Simple Harmonic Motion

Simple harmonic motion (SHM) is a type of oscillatory motion where the restoring force is directly proportional to the displacement from an equilibrium position and opposite in direction. The motion is typically sinusoidal in time and represented by functions like cosine or sine, making it predictable and periodic.

Potential Energy in SHM

In the context of SHM, the potential energy stored in the system is related to the displacement of the particle and is usually given by a quadratic relationship, such as U = 1/2 kx², where k is the force constant. This means that the potential energy is maximum at the extreme displacements and minimum (usually zero) at the equilibrium position.

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