KD3203 2020-12-20 21:23
SHM’s oscillation under conditions
Moving to and fro about equilibrium position
Acceleration’s directly proportional
And opposite to displacement from equilibrium
Angular frequency times x is the a
Can vertically project circular motion
Displacement is amplitude times sin omega t
Differentiate for the v, one more for the a
Rotating vector model, v x a in concentric circle
Describes phase difference, connects it to circular
When mass connected to spring has no friction
Horizontal, Hooke's law, vertical, mg-k(e+x)
T equals, 2π root m over k
Natural length or mg/k is equilibrium
T is mg cos theta, force minus mg sin (theta)
Theta's x by l, omega root g by l
T equals 2π the square root of l over g
Pendulum period only depends on length
By EPE total energy is half kA square
Conservation shows max KE, PE the same
The total energy independent of time and x
Changes from KE to PE, harmony