The total energy of the body executing S.H.M is E. Then the kinetic energy when the displacement is half of the amplitude is αE Find the value of α.Correct answer is '0.75'. Can you explain this answer?

Question

The total energy of the body executing S.H.M is E. Then the kinetic energy when the displacement is half of the amplitude is &alpha;E Find the value of &alpha;.Correct answer is '0.75'. Can you explain this answer?

Answer

In simple harmonic motion (SHM), the total mechanical energy of the system is constant and is equal to the sum of the potential energy and kinetic energy at any given point.

E = PE + KE

When the displacement is half of the amplitude, the potential energy is at its maximum, and the kinetic energy is at its minimum. This is because at the extreme points of the motion (where the displacement is equal to the amplitude), the potential energy is zero and the kinetic energy is at its maximum.

Therefore, when the displacement is half of the amplitude, the potential energy is equal to the total energy, E.

PE = E

Since the total energy is constant, we can subtract the potential energy from the total energy to find the kinetic energy.

KE = E - PE
KE = E - E
KE = 0

Therefore, the kinetic energy when the displacement is half of the amplitude is zero.

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