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Show that x(t ) = x(initial)*cos(t) is a solution to the equation of motion for a harmonic oscillator, d^2x/dt^2 +2x =0.

Show that x(t ) = x(initial)*cos(ωt) is a solution to the equation of motion for a harmonic oscillator, d^2x/dt^2 +ω2x =0. To do this, write down the differential equation and then make substitutions for x and for its second derivative with respect to t using x(t)= x(initial)*cos(ωt), then simplify the resulting expression.
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