Question

In a simple harmonic motion. when the displacement is one-half the amplitude,what fraction of the total energy is kinetic?
A) Zero B) 1/4
C) 1/2 D) 3/4​

Answer 1

Answer:

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Answer 2

3/4 E is the ans !

E X P L A N A T I O N

Total energy of the particle executing

S.H.M at ins_tant t is given by

E = 1/2 mωa^2 _[i]

and kinetic energy of the particle at ins_tant t is given by

Ek = 1/2 mω^2 ( a^2 - x^2 ) _[ii]

When

x = a/2, Ek = 1/2 mω^2 [ a^2 - a^2 / 4 ]

x = 1/2 mω^2 × 3/4 a^2

Ek = 1/2 × 3/4 mω^2 a^2 _[iii]

From Eq [i] and [ii]

Ek / E = 3/4 => Ek = 3/4 E

∴ 3/4 Of the Total Energy is Kinetic !