Vibrational Motion

Fnet (pendulum)

(weight/length) (path distance) (W/L)S fnet = w sin theta w cosine theta = tension

frequency for a spring

1/T, 2piF = root (k/m)

max acceleration for a spring

A((root(k/m))^2) KA/m

acceleration of a mass on a spring

A(2piF)

Velocity at equilibrium position (for mass on a spring)=

A(rootK/m)

E total for mass on spring =

K block + U spring 1/2mv^2 + 1/2kx^2

Period for a spring

T = 2π√(m/k)

period of a pendulum

Tp=2π√l/g - shorter length, period goes down, frequency goes up, angle increases since it has to have the same energy over lesser height,

peak Us is

at the endpoints for a mass on a spring

speed of a pendulum depends on

only the distance it is pulled back (so height)

Vibrational motion is described by

period (time for one cycle), frequency (num of cycles a sec), and amplitude (maximum chnage from equilibrium)

all vibrational motion as a

restoring force - tension for a mass on a spring - gravity for a pendulum

Peak Kinetic energy is at

the equilibrium position for a mass on a spring

for an object on a spring in simple harmonic motion

uniform circular motion viewed from the side is simple harmonic motion

simple harmonic motion

vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium

we can treat vertical masses on springs as horizontal masses on springs if

we reference x eq as the starting height

for a mass on a spring, A =

x distance from equilibrium = max elongation

eqation for simple harmonic motion graph

x = Asin (2πft + Φ) + xeq Φ = phase constant, how far it is shifted