<Dd> ω = k m, A = c 1 2 + c 2 2, tan ⁡ φ = c 2 c 1, (\ displaystyle \ omega = (\ sqrt (\ frac (k) (m))), \ qquad A = (\ sqrt ((c_ (1)) ^ (2) + (c_ (2)) ^ (2))), \ qquad \ tan \ varphi = (\ frac (c_ (2)) (c_ (1))),) </Dd> <P> In the solution, c and c are two constants determined by the initial conditions, and the origin is set to be the equilibrium position . Each of these constants carries a physical meaning of the motion: A is the amplitude (maximum displacement from the equilibrium position), ω = 2πf is the angular frequency, and φ is the phase . </P> <P> Using the techniques of calculus, the velocity and acceleration as a function of time can be found: </P> <Dl> <Dd> v (t) = d x d t = − A ω sin ⁡ (ω t − φ), (\ displaystyle v (t) = (\ frac (\ mathrm (d) x) (\ mathrm (d) t)) = - A \ omega \ sin (\ omega t - \ varphi),) </Dd> </Dl>

Write the differential equation of simple harmonic motion