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

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

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