Question

The total energy of a particle executing S.H.M. is 80 J. What is the potential energy when the particle is at a distance of 3/4 of amplitude from the mean position

• A. 60 J
• B. 10 J
• C. 40 J
• D. 45 J

Answer 1

Answer: (D)

45 J

Answer 2

$\frac{U}{E} = \frac{\frac{1}{2}m\omega^{2}y^{2}}{\frac{1}{2}m\omega^{2}a^{2}} = \frac{y^{2}}{a^{2}}$⇒ $\frac{U}{80} = \frac{\left( \frac{3}{4}a \right)^{2}}{a^{2}} = \frac{9}{16}$⇒ $U = 45J$