2016:
The kinetic energy of a particle executing SHM is given by:
K = ½ mω²x²
where m is the mass of the particle, ω is the angular frequency of the oscillation, and x is the displacement of the particle from the equilibrium position.
The potential energy of a particle executing SHM is given by:
U = ½ mω²A² - ½ mω²x²
where A is the amplitude of the oscillation.
When the kinetic energy of the particle is equal to its potential energy, we have:
K = U
Substituting the expressions for K and U into this equation, we get:
½ mω²x² = ½ mω²A² - ½ mω²x²
Collecting like terms, we get:
x² = A²
Therefore, the displacement of the particle from the equilibrium position at which the kinetic energy is equal to the potential energy is equal to the amplitude of the oscillation.
2017:
