Download Simple Harmonic Motion (SHM)

Spring mass system
Energy
Dynamics
Kinematics
Simple Harmonic Motion (SHM)
Position as a function of time
x = A sin(ω t + ϕ0 )
x = A cos(ω t + ϕ0 )
Velocity as a function of time
v = A ω cos(ω t + ϕ 0 )
v = − A ω sin (ω t + ϕ0 )
Acceleration as a function of time
a = − A ω 2 sin(ω t + ϕ 0 )
a = − A ω 2 cos(ω t + ϕ0 )
Velocity as a function of position
v = ±ω
Acceleration as a function of position
Maximun velocity
a = −ω 2 x
v MAX = A ω
Maximun acceleration
a MAX = A ω 2
Hooke's Law
F=−kx
Relationship between spring constant,
angular frequency and mass
k = ω 2m
Maximun force
FMAX = k A,
Kinetic energy
EKIN =
Potential energy
Pendulum
Mechanical energy
ω
t
ϕ0
F
m
k
EKIN
EPOT
EMEC
f
L
g
T
A2 − x 2
FMAX = m ω 2 A
1
m v2 ;
2
1
EPOT = k x 2
2
1
EMEC = k A2
2
Period of swing of a simple gravity
pendulum
T ≅ 2π
Relationship between frequency, period and
angular frequency
f =
Symbol
x
v
a
A
www.vaxasoftware.com
EKIN =
(
1
k A2 − x 2
2
L
g
1
; ω =2π f
T
Magnitude
S.I. unit
Position
Velocity
Acceleration
Amplitude (maximum displacement)
Angular frequency
m
m/s
m / s2
m
rad / s
Time
Phase
s
rad
Force
Mass
Spring constant
Kinetic energy
Potential energy (spring)
Mechanical energy
Frequency
Length of the pendulum
Acceleration of gravity
Period
N
kg
N/m
J
J
J
Hz
m
m / s2
s
www.vaxasoftware.com
)