Transcript Slide 1

Period of a Mass on a Spring Post-Lab
T (s)
T (s)
Angle (degrees)
xm (m)
Period is independent of
the angle of the track
Period is independent of
Amplitude
Period of a Mass on a Spring Post-Lab
T (s)
T m
T   3.36 s   m
 

kg
m (kg)
Theoretica l slope for a spring constant of
k  3.5 N
T (s)
m  kg 
m
Period of a Mass on a Spring Post-Lab
Theoretical Derivation of the Period of a mass on the end of a spring
Frictionless
 xm
0

Fs
xm


Fs  kx

FN

Fg
Hooke’s Law
Linear Simple Harmonic Oscillator
FN  Fg
Period of a Mass on a Spring Post-Lab
Theoretical Derivation of the Period of a mass on the end of a spring
Frictionless
 xm

Fs
But
Hooke’s Law

Fg
xm
0


 Fx  max


Fs  ma


Fs  kx

FN

a   2 x

 kx  m   2 x
k  m 2
Angular
frequency of a
mass on the end
of a spring
Simple Harmonic Oscillator
Where
x  xm cost   
k

m

Period of a Mass on a Spring Post-Lab
Theoretical Derivation of the Period of a mass on the end of a spring
Frictionless
 xm
Angular
frequency of a
mass on the end
of a spring
But
0

Fs

Fg
xm
k

m
2

T

FN
2
k

T
m
Period of a mass
on the end of a
spring
m
Ts  2
k
Period of a Mass on a Spring Post-Lab
 m
T   3.36 s

kg


2 

Ts  

 k
m
Ts  2
k
m
Slope of the T vs. m graph
Theoretical  Experimental
% error 
100
Theoretical