FORMULA DERIVATION FOR
ENGINEERING & PHYSICS
INTRVIEW
Songyue Wang
, Formula Derivation for Engineering & Physics Interview
written by Songyue Wang
Simple Harmonic Motion
Displacement
x = x0 sin(ωt )
Velocity
dx
v
= = ω x0 cos(ωt )
dt
Acceleration
dv
a= ω 2 x0 (− sin(ωt )) =
= −ω 2 x
dt
Maximum velocity
v = ω x0 cos(ωt )
when cos(ωt ) = 1
vmax = ω x0
Another equation for velocity
= 0 sin(ω t ) and v
x x= ω x0 cos(ωt )
x v
= sin(
= ωt ) and cos(ωt )
x0 ω x0
x 2 v 2
( ) +( ) =
1
x0 ω x0
ω 2 x2 + v2 =
ω 2 x0 2
=v 2 ω 2 ( x0 2 − x 2 )
=v ω x0 2 − x 2
Period of mass-spring system (horizontal)
ENGINEERING & PHYSICS
INTRVIEW
Songyue Wang
, Formula Derivation for Engineering & Physics Interview
written by Songyue Wang
Simple Harmonic Motion
Displacement
x = x0 sin(ωt )
Velocity
dx
v
= = ω x0 cos(ωt )
dt
Acceleration
dv
a= ω 2 x0 (− sin(ωt )) =
= −ω 2 x
dt
Maximum velocity
v = ω x0 cos(ωt )
when cos(ωt ) = 1
vmax = ω x0
Another equation for velocity
= 0 sin(ω t ) and v
x x= ω x0 cos(ωt )
x v
= sin(
= ωt ) and cos(ωt )
x0 ω x0
x 2 v 2
( ) +( ) =
1
x0 ω x0
ω 2 x2 + v2 =
ω 2 x0 2
=v 2 ω 2 ( x0 2 − x 2 )
=v ω x0 2 − x 2
Period of mass-spring system (horizontal)
