Question

derive the equation for harmonic oscillation

Answer 1

we say that a motion is harmonic if it obeys

\[ a=- kx\] where a is acceleration and x is the displacement (from origin).. so you can form a differential equation from this in x

\[\frac{d^2x}{dt^2} + kx =0\]

solve this second order differential and get a function for x.. that is the derivation..

P.S hope u know how to solve that differential

Answer 2

then what's this equation x=Asin (wt-phi) ?

Answer 3

this is the solution to this DE, if you substitute that in this equation it satisfies it

Answer 4

so that isn't the equation for harmonic oscillation or motion?

Answer 5

this is equation of position as function in time. The equation of SHM is x'' + k/m x =0

Answer 6

i have an entire chapter about harmonic motion, i only see equations of this kind: x=Asin(wt-phi) etc..

Answer 7

i'm guessing i only need to write that equation if it's asked..

Answer 8

Then u don't have the derivation included.. :P

Answer 9

and an equation of position in function of time is what a harmonic oscillation is..right, describing the projected motion of a circular motion

Answer 10

i guess..

Answer 11

i'll close this post then

Answer 12

better ^_^