S h m by athar

400grams

200grams

FORCE

(N)

Extension

Slope = spring constant600grams

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Extension of spring

DEFINITION

When a body moves to and fro, about its position of equilibrium, along the same straight line so that it repeats its motion.

VIBRATORY MOTION

200grams

VibratingTuning fork

A weight ona spring

A boy on a swing

DEFINITION

If motion of a body is such that

•Its acceleration is always directed to the mean position.

•Acceleration is directly proportional to the displacement from mean position. Then body is said to be in state of Simple Harmonic Motion.

MASS ATTACHED TO A SPRING

Let’s consider a mass “m”

•attached to one end of the spring.

•Placed on horizontal surface

•On frictionless place

•The other end is fixed to a rigid body.

Consider figure “a”

•Mass-spring system is in equilibrium

•No extension in the spring

•Displacement is zero

•No force acting on it

Figure aDisplacement = 0Acceleration = 0

Net Force = 0

When an external force Fext is applied

Spring is extended Extension is denoted by “x” Position of spring changes from “o” to “a”

Figure b

Displacement = maxVelocity = 0

Net Force = maxAcceleration = maxKinetic Energy = 0

The relation between Fext and x can be given by using Hook's law i.e

Fext α x Fext = (constant) x

Fext = Kx

K = Fext / x

Where “K” is called Spring Constant. Its unit is N/m.

When spring is released then,External force becomes absent. It comes to its original length.This motion is due to ‘restoring force’

External ForceRestoring force

For restoring force Fre = - Kx

This force is the cause of acceleration in the mass “m”.By applying Newton’s law,

Fre = ma

Then ma = - Kx

a = - (k/m) x

from this relation we conclude that,

acceleration α - displacement

a α - x

Displacement = maxVelocity = 0

Acceleration = maxKinetic Energy = 0Net Force = max

Displacement = 0Velocity = max

Acceleration = 0Kinetic Energy = max

Net Force = 0

At point ‘a’

At mean position

At point ‘b’Displacement = max

Velocity = 0Acceleration = maxKinetic Energy = 0Net Force = max

S H M.avi

What we conclude is…….

A body executing simple harmonic motion, always vibrates about its mean position.

its acceleration is always directed towards its mean position.

its acceleration is directly proportional to displacement

Its velocity is maximum at the mean position and zero on the extreme positions.

Time Period of Mass spring system

For any object in simple harmonic motion, the time required to complete one cycle is the time period T.

T = 2π √ m / k

PROBLEM

A body of mass 0.5 kg is attached to a spring placed on a horizontal surface . If the spring constant is 8 N/m then find time period of a body.

SUMMARY

Vibratory motion Hook's law Simple Harmonic Motion Mass attached to a spring. Time Period

QUESTIONS

Define simple harmonic motion? Give examples of SHM? What is the formula to calculate time

period of a mass attached to a spring? What is the unit of spring constant?

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