SATHEE: Simple Harmonic Motion 1 Question 3

Simple Harmonic Motion 1 Question 3

3. A particle is executing simple harmonic motion (SHM) of amplitude $A$ , along the $X$ -axis, about $x = 0$ . when its potential energy (PE) equals kinetic energy (KE), the position of the particle will be

(2019 Main, 9 Jan II)

(a) $A$

(b) $\frac{A}{2}$

(d) $\frac{A}{\sqrt{2}}$

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Answer:

Correct Answer: 3. (d)

Solution:

Here, $A$ =amplitude of particle in SHM

We know that in SHM potential energy $(U)$ of a particle is given by the relation at distance $x$ from the mean position is

$U = \frac{1}{2} k x^{2}$

and at the same point kinetic energy $(K)$

$\begin{aligned} = Total energy - Potential energy \\ = \frac{1}{2} k A^{2} - \frac{1}{2} k x^{2} \end{aligned}$

According to the question,

potential energy $=$ kinetic energy

$\begin{aligned} ∴ & \frac{1}{2} k x^{2} & = \frac{1}{2} k A^{2} - \frac{1}{2} k x^{2} \\ or & k x^{2} & = \frac{k A^{2}}{2} or x = \pm \frac{A}{\sqrt{2}} \end{aligned}$

Simple Harmonic Motion 1 Question 3

3. A particle is executing simple harmonic motion (SHM) of amplitude $A$ , along the $X$ -axis, about $x = 0$ . when its potential energy (PE) equals kinetic energy (KE), the position of the particle will be

Answer:

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Simple Harmonic Motion 1 Question 3

3. A particle is executing simple harmonic motion (SHM) of amplitude A, along the X-axis, about x=0. when its potential energy (PE) equals kinetic energy (KE), the position of the particle will be

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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3. A particle is executing simple harmonic motion (SHM) of amplitude $A$ , along the $X$ -axis, about $x = 0$ . when its potential energy (PE) equals kinetic energy (KE), the position of the particle will be