Question

What is simple harmonic motion and its derivation?

Answer 1

a form of periodic motion of a particle, etc, in which the acceleration is always directed towards some equilibrium point and is proportional to the displacement from this point. Abbreviation: SHM
Deriving the Equation for Simple Harmonic Motion
Rearranging our equation in terms of derivatives, we see that:
m = - kx
or
+ x = 0 As a tentative solution, we write:
x = a cos(bt)
where a and b are constants. Differentiating this equation, we see that
= - ab sin(bt)
and
= - ab 2cos(bt)
Plugging this into our original differential equation, we see that:
- ab 2cos(bt) + a cos(bt) = 0
It is clear that, if b 2 = , then the equation is satisfied. Thus the equation governing simple harmonic oscillation is:
simple
x = a cos t