The solution is straightforward, simply take an Anzats of the formcoverband said:The equation of simple harmonic motion is given as
(d2x)/(dt2)+xk^2=0
Could someone show me HOW we arrive at the general solution to this second order ODE
Simple harmonic motion is a type of periodic motion in which a system oscillates back and forth around an equilibrium point. It is characterized by a restoring force that is proportional to the displacement from the equilibrium point and is in the opposite direction of the displacement.
Some examples of simple harmonic motion include a pendulum, a mass-spring system, and a bouncing ball. These systems exhibit simple harmonic motion because they have a restoring force that is proportional to the displacement from the equilibrium point.
Simple harmonic motion differs from other types of motion in that it is a periodic motion that is governed by a restoring force that is proportional to the displacement from the equilibrium point. It is also characterized by a constant period and amplitude.
The equation for simple harmonic motion is x(t) = A*sin(ωt + φ), where x is the displacement from the equilibrium point, A is the amplitude, ω is the angular frequency, and φ is the phase angle.
In simple harmonic motion, the total energy of the system is conserved and is equal to the sum of the kinetic energy and potential energy. As the system oscillates between the equilibrium point and the maximum displacement, the energy is constantly being converted between these two forms.