Question

The potential energy of a particle executing S.H.M. is 2.5 J, when its displacement is half of amplitude. The total energy of the particle be

• A. 18 J
• B. 10 J
• C. 12 J
• D. 2.5 J

Answer 1

Answer: (B)

10 J

Answer 2

$\frac{\text{Potential energy }(U)}{\text{Total energy }(E)} = \frac{\frac{1}{2}m\omega^{2}y^{2}}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}}$

So $\frac{2.5}{E} = \frac{\left( \frac{a}{2} \right)^{2}}{a^{2}}$ ⇒ $E = 10J$

⇒ $E = 10J$)