Physics 1 Lab 10: Simple Pendulum

The final derived formula for the Period (T) of a Simple Pendulum based on the SHM approximation

T= 2π sqr(L/g)

The expression do the angular frequency (ω) of a simple pendulum

ω= sqr(g/L)

a=

-ω²x

ax for small angles=

-g/Lx

The equation for the x-component of acceleration (ax​) for a simple pendulum before the small-angle approximation

ax=-gsinθ

The small-angle approximation that allows the pendulum to be modeled as Simple Harmonic Motion (SHM)

sinθ=θ= x/L

The maximum initial angle (in degrees) used in the pre-lab calculation for the small-angle error

0.25 radians, 14. 3 degrees

x under small angle approximation =

Lsinθ= Lθ

Δx=

LΔθ

The plot and resulting slope needed to find the local value of g (acceleration due to gravity)

Plot T² vs. L, results is 4pi²/g

The equation used to calculate the percent error of the small-angle approximation (sinθ=θ)

(θ)-(sinθ)/sin(θ) x100

The equation for the y-component of acceleration (ay) for a simple pendulum before the small-angle approximation

T-gcosθ

what happens as the job swings through the electronic counter ?

it measures the acceleration after three swings(1 rotation)

what type of function does T vs. θinitial create

a polynomial

what should the intercept of T vs. θinitial make

2pi sqroot(L/g)

what does the intercept of T vs. θinitial mean

it is the initial T without dependency on theta

what type of motion does pendulum execute under small angles ?

simple harmonic motion

what does the y intercept of T(θ) represent ?

the period at θ=0=2π sqroot(L/g)

in the y direction what forces act on the pendulum bob?

tension t and mgcosθ