Question
Download Solution PDFThe total energy of the body executing SHM is E. The kinetic energy is one-third of the total energy when the displacement of the body having amplitude (a) is _______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- The total energy in simple harmonic motion is the sum of its potential energy and kinetic energy.
- The law of conservation of energy states that energy can neither be created nor destroyed. Therefore, the total energy in simple harmonic motion will always be constant
Total energy = kinetic energy + potential energy
Total energy in S.H.M. is ET = ½ m ω2 a2; where a = amplitude, m = mass
Potential energy P.E. = ½ m ω2 y2 , where y = displacement
Kinetic energy K.E. = ½ m v2, where v is the velocity of the wave.
CALCULATION:
- Total energy = kinetic energy + potential energy
Given that:
The total energy in S.H.M. is given by:
Where a = amplitude, m = mass
Potential energy is given by:
Where y = displacement
The total energy is:
⇒ ET = K.E.+ P.E
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