# A particle is vibrating in S.H.M. with an amplitude of 4 cm. at what displacement from the equilibrium position is its energy half potential and half kinetic?

Vikas TU
14149 Points
3 years ago

Total energy E= potential energy+ kinetic energy.

Now, given that potential energy = kinetic energy=(1/2)E.

Now, E=(1/2)kA^2. Where, k is force constant and A is amplitude. A=4 cm given.

Next, potential energy at displacement x is(1/2)kx^2.

Therefore (1/2)kx^2=(1/2)(1/2)kA^2 OR

x^2=(1/2)A^2=(1/2)(4)^2=8 OR

x=sqrt(8)cm.
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