Concept:
- Simple Harmonic Motion (SHM): The Simple Harmonic Motion is studied to discuss the periodic Motion Mathematically.
- In Simple Harmonic motion, the motion is between two extreme points, and the restoring force responsible for the motion tends to bring the object to mean position.
- The motion of a Simple pendulum and a block attached to spring are common examples of SHM.
Mathematically, SHM is Defined as:
x = A Sin (ωt + ɸ),
x is the displacement of the body from mean Position, at time t. ɸ is phase Difference.
A is Amplitude of Motion, that is the Maximum distance the body in SHM can move from mean Position.
ω is Angular Speed =
T is the time period of Motion,
- Potential Energy of the body in SHM is
P =
- Kinetic Energy of the body in SHM is
K =
- Total Energy of the Body in SHM (E)
E=
Calculation:
Given,
Potential Energy = Kinetic Energy at some displacement x from mean position.
=
⇒
⇒
⇒
⇒
So, Option A / √ 2 is the correct option.
Additional Information
- Potential Energy is maximum at Extreme positions while Kinetic Energy is Maximum at mean Position.
- Potential Energy is zero at mean Position while Kinetic Energy is zero at Extreme Positions.
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