Calculation Example – Simple harmonic vibration part1

A single point with mass m is vibrating harmonically. The displacement x from point of balance is governed by the differential equation

where ω is a positive constant.

a) Show that

and

are equivalent.

Solution

So the form is                 x(t)=A sin⁡ωt+B cos⁡ωt

where

                       x(t)=A sin⁡ωt+B cos⁡ωt

with