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Oscillations - Part 01
Time period (T) The time interval after which the motion repeats itself.
Periodic Motion Motion that repeats itself in equal intervals of time.
v(t) = -ωA cos ( ωt + Φ )
k = mω2F(t) = -kA cos ( ωt + Φ )
a(t) = -ωA2 cos ( ωt + Φ )
ωA = -Velocity Amplitude
• SHM is the simplest form of oscillatory motion.
• Force on the oscillating body α
Displacement from the mean position
• Direction of the force is always towards the mean position.
Frequency (ν) The number of repetitions per unit time. ν = 1T
v(t) = x(t)ddT
a(t) = v(t)ddT
f(t) = A sin ωt + B cos ωt
f(t) = D sin ( ωt + Φ )Φ = tan-1 BAD = A2 + B2
Low frequency Oscillatory motion
High frequency Vibration
Simple Harmonic Motion (SHM)
Oscillatory motion Repeated to and fro motion of an object.
Velocity & Acceleration in SHM
Force acting on a particle executing SHM
Represent Periodic function as sine and cosine functions
x(t) = A cos ( ωt + Φ )
Φ = Phase constant
x(t) = Displacement A = Amplitude
ω = Angular frequency = π4
SHM is represented by the equation
π2Velocity lags displacement by a phase angle of .
Acceleration lags displacement by a phase angle of π.
ωt + Φ
y
ωA
ωt + Φ
v(t)O P’
P
T
+A
x
-A
0
+ωA
-ωA
0
+ω2A
-ω2A
Acc
eler
atio
nVe
loci
tyD
ispl
acem
ent
0
(a)
(b)
(c)
t
t
t
π4Φ = -
Φ = 0
4
3+A
-A
0
Dis
plac
emen
t
t