What is the ratio between the potential energy and the total energy of the particle executing SHM when its displacement is half of its amplitude?

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1. The total energy of the particle is four times its potential energy.
2. The total energy of the particle is two times its potential energy.
3. The total energy of the particle is equal to its potential energy.
4. The total energy of the particle is half of its potential energy.

Option 1 : The total energy of the particle is four times its potential energy.

The correct answer is option 1) i.e. The total energy of the particle is four times its potential energy.

CONCEPT:

• Simple harmonic motion (SHM): It is a type of oscillatory motion in which the restoring force is directly proportional to the displacement of the body from its mean position.​
• The energy in simple harmonic motion: 
  •  The total energy of a particle executing SHM is the sum of its kinetic and potential energy.

The kinetic energy is given by the equation: 

The potential energy is given by the equation: 

The total energy, E = KE + PE

Where m is the mass, ω is the angular frequency, y is the displacement of the particle from the mean position and a is the amplitude.

EXPLANATION:

Given that:

Displacement is half the amplitude ⇒ y = a/2

Ratio 

Thus, the total energy is four times the potential energy.

Let's discuss the concepts related to Oscillations and Energy in Simple Harmonic Motion. Explore more from Physics here. Learn now!

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• Mechanical Properties Of Fluids

Dear Student,

Total energy=mA2ω22U=mA2ω22sin2ωtU at x=A2=Asinωtsinωt=0.5ratio ,mA2ω22sin2ωtmA2ω22=0.52=0.25Regards

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