Question

The total energy of a particle, executing simple harmonic motion is. where x is the displacement from the mean position, hence total energy is independent of x.

Answer 1

Answer:

harmonic motion, x(t)=Acos(ωt+ϕ). Therefore,

Potential energy, U=

2

1

kx

2

=

2

1

kA

2

cos

2

(ωt+ϕ)

Kinetic energy, K.E=

2

1

mv

2

=

2

1

m(

dt

dx

)

2

=

2

1

kA

2

sin

2

(ωt+ϕ)

Now, Total energy

E=U+K.E

=

2

1

kA

2

cos

2

(ωt+ϕ)+

2

1

kA

2

sin

2

(ωt+ϕ)

=

2

1

kA

2

Therefore, total energy is independent of x.