The one-dimensional simple harmonic oscillator is described by the differential equation \begin{equation} m\frac{d^2x}{dt^2}+kx=0 \end{equation} Here \(m\) is the mass of the particle and \(k\) is the constant characterizing the restoring force. Solution of the simple harmonic oscillator The solution satisfying the initial condition \(x(0)=A\), where \(A\) is the amplitude of the oscillations, is given by