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​

Answer 1

Given :

• Potential energy of the particle = 2.5 J

To Find :

• Total enery of the particle when displacement becomes half

Solution :

$\tt Potential \: energy = \frac{1}{2}m { \omega }^{2} {y}^{2} \\ \\ \tt Total \: enery =\frac{1}{2} { \omega}^{2} {a}^{2} \\ \\ \boxed{ \purple{ \tt \frac{Potential \: Energy \: (U)}{total \: energy \: (E)} = \frac{ \frac{1}{2}m { \omega }^{2} {y}^{2} }{ \frac{1}{2} { \omega}^{2} {a}^{2} } = \frac{ {y}^{2} }{ {a}^{2} } }}$

$\tt \dfrac{2.5}{E} = \frac{ { \big(\frac{a}{2} \big) }^{2} }{ {a}^{2} } \\ \\ \tt \frac{2.5}{E} = \frac{\frac{{a}^{2}}{4}}{{a}^{2}}\\ \\ \tt E= 2.5 \times 4 \\ \\ \large \boxed{ \tt \blue{ Energy = 10 \: J}}$