The particle executing simple harmonic motion has a kinetic energy of . The maximum values of the potential energy and the total energy are respectively.

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Q.

The particle executing simple harmonic motion has a kinetic energy of . The maximum values of the potential energy and the total energy are respectively.

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a

and

b

0 and

c

and

d

and

answer is A.

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Detailed Solution

Concept- The above equation represents simple harmonic motion. When a force is given to an item and that object moves with respect to the mean position, simple harmonic motion occurs. The applied force in simple harmonic motion is directly proportional to the displacement of the object. As a result, the maximum potential energy will be found at the maximum displacement. We may calculate total energy from potential energy using the law of conservation of energy.
Below is an energy diagram of a basic harmonic motion.
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At the extreme points, the kinetic energy is zero and the potential energy is highest, according to basic harmonic motion.
= total energy + Kinetic energy Potential power
As a result, at extreme points, total energy equals potential energy.
The maximum energy is represented by

in the above equation of simple harmonic motion. The maximum value of sinusoidal functions is 1.
As a result, at extreme points, the greatest potential energy is

.
Because the maximal potential energy is

,the total energy will be

. as well.
As a result, A is the correct answer.
Additional information: Simple harmonic motion is a type of motion in which the object's acceleration is always directly proportional to the distance from its path's centre. This acceleration is always aimed at the centre.
Because simple harmonic motion is comparable to circular motion, the potential energy can be expressed as follows:

, where

is the mass of the object,

is the angular frequency and

is the displacement.
At the maximum displacement, the potential energy will be the total energy.

, where A is the amplitude (maximum displacement).
Kinetic energy can be written as,

, where

is the mass of the object and

is the velocity of the object.
Hence the total energy can be written as,

Angular frequency can be written as,

This equation can be used to calculate the velocity of an object in simple harmonic motion at any point.
Hence, the correct answer is option 1.

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