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What is the total energy (T.E.) in simple harmonic motion?

  • a)
    T.E. = K.E. + P.E.

  • b)
    T.E. = P.E.

  • c)
    T.E. = K.E.

  • d)
    T.E. = K.E. - P.E.

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the total energy (T.E.) in simple harmonic motion?a)T.E. = K.E...
The total energy (T.E.) in simple harmonic motion is the sum of its kinetic energy (K.E.) and potential energy (P.E.), given by T.E. = K.E. + P.E.
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What is the total energy (T.E.) in simple harmonic motion?a)T.E. = K.E...

Total Energy in Simple Harmonic Motion

To understand the total energy in simple harmonic motion, we need to consider both kinetic energy (K.E.) and potential energy (P.E.).

Kinetic Energy (K.E.)
Kinetic energy is the energy an object possesses due to its motion. In the case of simple harmonic motion, the object oscillates back and forth with a certain velocity. The formula for kinetic energy is 1/2 * mass * velocity^2.

Potential Energy (P.E.)
Potential energy is the energy stored in an object due to its position or state. In simple harmonic motion, potential energy is stored in the spring or restoring force that causes the oscillation. The formula for potential energy in simple harmonic motion is 1/2 * k * x^2, where k is the spring constant and x is the displacement from the equilibrium position.

Total Energy (T.E.)
The total energy in simple harmonic motion is the sum of kinetic energy and potential energy. This is because the energy of the system remains constant throughout the motion due to the conservative nature of the restoring force. Therefore, the total energy can be calculated using the formula:
T.E. = K.E. + P.E.

By adding the kinetic energy, which is related to the velocity of the object, to the potential energy, which is related to the position of the object, we get the total energy of the system in simple harmonic motion. This total energy remains constant throughout the motion, oscillating between kinetic and potential forms.
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