The potential energy of a simple harmonic oscillator of mass =2 kg in its mean position is 5 J . If its total energy is 9 J and its amplitude is 0.01 m , its time period would be:

Question

The potential energy of a simple harmonic oscillator of mass =2 kg in its mean position is 5 J . If its total energy is 9 J and its amplitude is 0.01 m , its time period would be: (A) (π /10)s (B) (π /20)s (C) (π /50)s (D) (π /100)s

Tardigrade Admin · Accepted Answer

P.E.=5J, T.E.=9J Using mechanical energy conservation T.E. =P.E. +K.E. 9=5+K.E. ⇒ K.E.=4 (Maximum) K.E.m a x at mean position =(1/2)ω 2A2m 4=(1/2)× 2× ((2 π /t))2× (1/100)× (1/100) T2=(π 2/100 × 100) T=(π /100)s

Q. The potential energy of a simple harmonic oscillator of mass $= 2 k g$ in its mean position is $5 J$ . If its total energy is $9 J$ and its amplitude is $0.01 m$ , its time period would be:

$\frac{π}{10} s$

$\frac{π}{20} s$

$\frac{π}{50} s$

$\frac{π}{100} s$

Q. The potential energy of a simple harmonic oscillator of mass =2kg in its mean position is 5J . If its total energy is 9J and its amplitude is 0.01m , its time period would be:

10π​s

20π​s

50π​s

100π​s

P.E.=5J,T.E.=9J Using mechanical energy conservation T.E.=P.E.+K.E. 9=5+K.E. ⇒K.E.=4 (Maximum) K.E.max​ at mean position =21​ω2A2m 4=21​×2×(t2π​)2×1001​×1001​ T2=100×100π2​ T=100π​s

Q. The potential energy of a simple harmonic oscillator of mass $= 2 k g$ in its mean position is $5 J$ . If its total energy is $9 J$ and its amplitude is $0.01 m$ , its time period would be:

$\frac{π}{10} s$

$\frac{π}{20} s$

$\frac{π}{50} s$

$\frac{π}{100} s$