Scribd
Upload
155 views1 page

Simple Harmonic Motion Basics

Simple harmonic motion (SHM) is the simplest form of oscillatory motion where the restoring force on an object is directly proportional to the displacement from the equilibrium position. SHM can be represented by the equation x(t) = A cos(ωt + Φ), where x(t) is the displacement at time t, A is the amplitude, ω is the angular frequency, and Φ is the phase constant. The velocity and acceleration of an object in SHM can also be expressed as functions of displacement using the angular frequency and phase constant.

Uploaded by

Joseph ndirangu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
155 views1 page

Simple Harmonic Motion Basics

Simple harmonic motion (SHM) is the simplest form of oscillatory motion where the restoring force on an object is directly proportional to the displacement from the equilibrium position. SHM can be represented by the equation x(t) = A cos(ωt + Φ), where x(t) is the displacement at time t, A is the amplitude, ω is the angular frequency, and Φ is the phase constant. The velocity and acceleration of an object in SHM can also be expressed as functions of displacement using the angular frequency and phase constant.

Uploaded by

Joseph ndirangu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

Oscillations - Part 01

Periodic Motion Motion that repeats itself in equal intervals of time.

Time period (T) The time interval after which the motion repeats itself.
Frequency (ν) The number of repetitions per unit time. ν = 1T
Oscillatory motion Repeated to and fro motion of an object.
Low frequency Oscillatory motion
High frequency Vibration

Simple Harmonic Motion (SHM)


• 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.


SHM is represented by the equation
Φ=- π 4
x(t) = A cos ( ωt + Φ ) 4
Displacement

+A
0 3 t
x(t) = Displacement A = Amplitude
ω = Angular frequency = π
-A
4 Φ = Phase constant Φ=0

Velocity & Acceleration in SHM


y

ωA v(t) = -ωA cos ( ωt + Φ ) v(t) = d x(t)


ωt + Φ
dT
ωA = -Velocity Amplitude
P

ωt + Φ a(t) = -ωA2 cos ( ωt + Φ ) a(t) = d v(t)


O P’
dT
v(t) x
Displacement

+A
0 t
-A
T
+ωA
Velocity lags displacement by a phase angle of π .
(a)
Velocity

2 0 t

Acceleration lags displacement by a phase angle of π. -ωA


(b)
+ω2A
Acceleration

0 t

-ω2A (c)

Force acting on a particle executing SHM


F(t) = -kA cos ( ωt + Φ ) k = mω2

Represent Periodic function as sine and cosine functions


f(t) = A sin ωt + B cos ωt
D = A2 + B2 Φ = tan-1 B
f(t) = D sin ( ωt + Φ ) A

You might also like