A body is said to be vibrating if it moves ——————- and ——————- or ——————- and —————– about a point.

Another term for vibration is ——————-.

A special kind of vibratory or oscillatory motion is called the ————————————- motion (SHM), which is the main focus of this chapter.

We will discuss important characteristics of SHM and systems executing SHM. We will also introduce different types of waves and will demonstrate their properties with the help of ————————————-.


In the following sections we will discuss simple harmonic motion of different systems. The motion of mass attached to a spring on a ————————————- surface,

the motion of a ball placed in a bowl and the motion of a bob attached to a ————————————- are examples of SHM.


One of the simplest types of oscillatory motion is that of ————————————————————————-(Fig,10.1). If the spring is stretched or compressed through a small displacement x from its mean position, it exerts a force F on the mass.

According to Hooke’s law this forrce is directly proportional to the change in ————————————- of the spring i.e.,


where ——————-is the displacement of the mass from its mean position ——————-, and k is a constant called the spring constant defined as——————-  :

The value of k is a measure of the stiffness of the spring, Stiff springs have large value of k and soft springs have small value of k.

As F=

Therefore, k =


or a =


a——————-  – X …….. (10.2)

lt means that the acceleration of a mass attached to a spring is directly proportional to its displacement from the mean position. Hence, the ——————————————————- is an example of simple harmonic motion.


The negative sign in Eq, 10.1 means that the force exerted by the spring is always directed opposite to the displacement of the mass. Because the spring force always acts towards the mean position, it is sometimes called a ————————————-.

A restoring force always pushes or pulls the object performing oscillatory motion towards the ——————- position.

Initially the mass m is at rest in mean position O and the resultant force on the mass is zero (Fig.10.1-a).

Suppose the mass is pulled through a distance x up to extreme position A and then released (Fig,10,1-b). The restoring force exerted by the spring on the mass will pull it towards the mean position `O. Due to the restoring force the mass moves ——————–, towards the mean position O. The magnitude of the restoring force ——————- with the distance from the mean position and becomes zero at O.

However, the mass gains speed as it moves towards the mean position and its speed becomes ——————- at O.

Due to ——————- the mass does not stop at the mean position O but continues its motion and reaches the extreme position B.

As the mass moves from the mean position O to the extreme position B, the restoring force acting on it towards the mean position steadily increases in strength.

Hence the speed of the mass ——————- as it moves towards the extreme position B. The mass finally comes briefly to rest at the extreme position B (Fig. 10.1-c). Ultimately the mass returns to ——————- position due to the restoring force.

This process is repeated, and the mass continues to oscillate back and forth about the mean position O. Such motion of a mass attached to a spring on a horizontal frictionless surface is known as Simple Harmonic Motion (SHIVI).

The time period T of the simple harmonic motion of a mass

‘m’ attached to a spring is given by the following equation:

T = ——————-(10.3)

P: 4


The motion of a ball placed in a bowl is another example of simple harmonic motion (Fig 1O,2).

When the ball is at the mean position O, that is, at the centre of the bowl net force acting on the ball is ——————–. ln this position, `weight` of the ball acts ——————- and is equal to the ——————- normal force of the surface of the bowl.

Hence there is no ——————-. Now if we bring the ball to position A and then release it, the ball will start moving towards the mean position ,————————————- to the restoring force caused by its weight.

At position Othe ball gets maximum speed and due to inertia it moves towards the extreme position B, While going towards the position B, the speed of the ball decreases due to the restoring force which acts towards the mean position.   the position B, the ball stops for a while and then again ——————————————————– mean position O under the action of there storing force;  is to and fro motion of the ball continues about the ——————-position p till all its energy is lost due to friction. Thus the ————————————- motion of the ball about a mean position placed in a bowl is an example of simple harmonic motion.


A simple pendulum also exhibits ——————-. it consists of a small bob of mass ‘m’ suspended from a light string of length ‘lf fixed at its ——————- end.

In the equilibrium position O, the net force on the bob is ——————- and the bobs is stationary. Now if we bring the bob to extreme position A, the net force is, ——————- zero [Fig,10.3). There is no force acting along the string as the tension in the string cancels the component of————————————- mg cos (J, Hence there is no motion along this ————————————-.

The component of the weight mg sin H is————————————- towards the mean position and acts as a ————————————- force.

Due to this force the bob starts moving towards the mean position 0. At O, the bob has got the maximum ——————- and due to ——————-, it does not stop at O rather it continues to. move towards _the extreme position B. During its motion towards point B, the velocity of the bob decreases due to restoring force. The velocity of the bob becomes ——————- as it reaches the ——————-.,


The restoring force ——————- still acts towards the mean position O and ——————- to this force the bob again starts moving towards the mean position O. In this way, the bob continues its ——————- motion about the mean position of It is clear from the above discussion that the speed of the bob increases while moving from point ———–to————————– due to the restoring force which acts towards O. Therefore, acceleration of the bob is also directed towards O.

Similarly, when the bob moves from O to B, its speed decreases due to restoring force which again acts towards O. Therefore, acceleration of the bob is again directed towards O. it follows that the acceleration of the bob’ is always directed towards the ——————- position O. Hence the motion of a simple pendulum is SHM.

We have the following formula for the time period of a simple pendulum

T =————————————- (10.4)

From the motion of these simple systems, we can define SHIVI


Simple harmonic- motion occurs when the net force is ——————————————————-to the displacement from  the ————————————- position  :and  is always directed towards ————————————-

In other words, when an object ————————————- about a fixed position (mean position) such that its acceleration is ——————- proportional to its displacement from the mean position and is always directed towards the mean position, its motion is

called ————————————-

important features of SHM are summarized as:

i, A body executing SHM always ——————- about a fixed position,

  1. its acceleration is always ——————- towards the mean position.

iii. The ————————————- of acceleration is always directly proportional to its displacement from the mean


position i.e., acceleration will be ——————- at the mean position while it will be maximum at the ——————- positions.

  1. its velocity is maximum at the mean position and zero at the extreme positions.

Now we discuss different terms which characterize simple harmonic motion.

VIBRATION: One complete round trip of a ——————- body about its mean position is called one vibration.

————————————-time taken by a vibrating body to complete one vibration.

Frequency (——————-)   The number of vibrations or cycles of a vibrating body in one second is called its frequency. It is ——————- of time period i.e., f=

amplitude (A); The ——————- displacement of a vibrating body on either side from its mean position is called its amplitude,


Find the time period and frequency of a simple pendulum 1.0m long ata location where g=10.0 ms2














Vibratory motion of ideal systems in the absence of any ——————- or ——————- continues indefinitely under the action of a restoring force.

Practically, in all systems, the force of friction ——————- the motion, so the systems do not oscillate ——————-. The friction reduces the mechanical energy of


the system as time passes, and the motion is said to be ——————-, This ——————- ——————- reduces the amplitude of the vibration of motion as shown in Fig. 10.4.

————————————- in automobiles are one practical application of damped motion. A ————————————- consists of a piston moving through a liquid such as oil (Fig.1O.5). The upper part of the shock absorber is firmly attached to the body of the car,

When the car travels over a bump on the road, the car may vibrate violently. The shock absorbers damp these vibrations and convert their energy into heat energy of the oil. Thus



Waves play an important role in our daily life. lt is because waves are carrier of ——————- and ——————- over large ——————-. Waves require some ——————- or ——————- source.

Here we demonstrate the ——————- and ——————- of different waves with the help of vibratory motion of objects.


Dip one end of a pencil into a tub of water, and move it ——————- and ——————- vertically (Fig. 10,6). The disturbance in the form of ripples produces water ——————-, which move ——————- from the source. When the wave reaches a small piece of cork

floating near the disturbance, it moves up and down about its original position while the wave will travel outwards. The net displacement of the cork is ——————-. The cork repeats its ——————- motion about its ——————- position.

ACTIVITY 10.2 Take a rope and mark a point P on it. Tie one end of the rope with a support and stretch the rope by holding its other end in your hand (Fig. 10.7). Now, flipping the rope ——————- and ——————- regularly will set up a wave in the rope which will travel towards the ——————- end. The point P on the rope will start ——————- up and down as the wave passes ——————- it. The motion of point P will be ——————- to the direction of the motion of wave. is placement


From the above simple activities, we can define wave as:

A wave is——————————————————————————————————————————————————————————————————————————————-

There are two categories of waves:

  1. ——————————————————-
  2. ————————————————————————-

1——————-Waves: which——————————————————————————————————————————————————————————————————–

Examples of mechanical waves are water waves, sound waves and waves produced on the strings and springs.

2————————————-waves:  which————————————————————————————————————————————————————————————————-

——————- waves, ——————- waves, ——————–,——————- and ——————- waves are some examples of electromagnetic waves.


Depending upon the direction of displacement of med\um with respect to the direction of the propagation of wave itself, mechanical waves may be classified as

————————————– waves can be produced on a spring (slinky) placed on a smooth floor or a long bench. Fix one end of the  ——————- or ——————-.

slinky with a rigid support and hold the other end into your hand. Now give it a regular ——————- and ——————- quickly in the direction of its length (Fig.10.8).


A series of disturbances in the form of waves will start moving along the length of the slinky. Such a wave consists of ——————- called ————————————- where the ——————- of the spring are ——————- together, alternating with regions called ————————————- (expansions) where the loops are spaced apart In the regions of

——————- particles of the ——————- are closer together while

in the regions of ——————-, particles of the medium are spaced apart The distance between two ——————- compressions is called wavelength The ————————————- and ——————- move back and forth along the direction of motion of the wave Such a

wave IS called ————————————————————————-

We can produce transverse waves with the help of a slinky Stretch out a sl|nl<y along a smooth floor with one end fixed Grasp the other end of the slinky and ————————————- quickly (Fig 10 9)

A wave in the form of alternate ——————- and ——————- will start travelling towards the fixed end the crestsare the highest points while the troughs are the lowest points

ofthe particles ofthe medium from the mean position The

distance between two ——————- crests or ——————- is called



Therefore, transverse waves can be defined as:

In case of transverse waves,————————————————————————————————————————————————————————————————————————————————————————————————————————————–

Waves on the surface of water and light waves are examples of transverse waves.


Energy can be transferred from one ——————- to another through ——————-. For example, when we shake the stretched string ——————- and ——————-, we provide our ——————- energy to the string. As a result, a set of waves can be ——————- travelling along the string.

The vibrating force from the hand ——————- the ——————- of the string and sets them in motion. These particles then transfer their energy to the ————————————– particles in the string. Energy is thus transferred from one place of the medium to the other in the form of ——————-.

The amount of energy carried by the wave depends on the distance of the stretched string from its rest position. That is, the energy in a wave depends on the amplitude of the wave, If we shake the string ——————-, we give more energy per ——————-

to produce wave of ——————- frequency, and the wave delivers more energy per second to the particles of the string as it moves ——————-.

Water waves also transfer energy from one place to another


as explained below:

ACTIVITY 10-32 Drop a stone into a pond of water. Water waves will be produced on the surface of water and will travel outwards (Fig. 1010). Place a ——————- at some distance from the falling——————-. When waves reach the cork, it will move up and down along with the motion of the water particles by getting energy from the waves.


This activity shows that water waves like other waves transfer energy from one place to another without transferring matter, i.e, water



Wave is a disturbance in a medium which travels from one place to another and hence has a specific velocity of travelling.

This is called the velocity of wave which is defined by

Velocity = ————————————-


If time taken by the wave in moving from one point to another is equal to its time period T, then the distance covered by the wave will be equal to one wave length, hence we can write:


But time period T, is reciprocal of the frequency f, i.e., T =——————-



Therefore, . V=————————————-(10.5)

Eq. (10.5) is true both for ——————- and ——————- waves,

EXAMPLE: 10.2 A wave moves on a slinky with frequency of 4 Hz and wavelength of0.4 m, What is the speed of the wave?


Given that, f =







Ripple tank is a device to produce water ——————- and to study their ——————-.

This apparatus consists of a rectangular tray having glass bottom and is placed nearly ——————- metre above the surface of a table (Fig. 10.11). Waves can be produced on the surface of water present in the tray by means of a vibrator (————————————-).









This vibrator plate over surface of water. On setting the vibrator ON, this ——————-

plate starts vibrating to generate water waves consisting of straight wave fronts (Fig,10,12). An ——————- bulb is hung above the tray to observe the image of water waves on the paper or screen, The crests and troughs of the waves appear as——————-and ——————–? lines respectively, on the screen.

Now we explain the reflection of water waves with the help of ripple tank.


Place a ——————- in the ripple tank. The water waves will reflect from the barrier. If the barrier is placed at an angle to the Wave front, the reflected waves can be seen to obey the law of reflection Le., the angle of the incident wave along the normal will be equal to the angle of the reflected wave

(Fig.10.13). Thus, we define reflection of waves as:



The speed of a wave in water depends on the ——————- of water If a block is submerged in the ripple tank, the depth of water in the tank will be ——————- over the block than elsewhere.

When water waves enter the region of ——————- water their wavelength ——————- (Fig,10.14). But the frequency of the water waves remains the ——————- in both parts of water because it is equal to the frequency of the vibrator









For the observation of refraction of water waves, we repeat the above experiment such that the boundary between the deep and the shallower water is at some angle to the wave front (Fig. 10.15).

Now we will observe that in addition to the change in wavelength, the waves change their ——————- of ——————- as well. Note that the direction of propagation is always ——————- to the wave ——————-. This change of path of water waves while passing from a region of deep water to that of ——————- one is called refraction which is defined as:


When a wave ————————————————————————————————————————————————- of travel changes.

Now we observe the phenomenon of ——————- of water waves.

Generate straight waves in a ripple tank and place two ——————- in line in such a way that separation between them is equal to the ——————- of water waves. After passing through a small ——————- between the two obstacles, the waves will spread in every

——————- and change ——————————————————- pattern (Fig. 10.16).

Diffraction of waves can only be observed clearly if the size of the obstacle is comparable with the wavelength of the wave.

Fig.10.17 shows the diffraction of waves while passing through a slit with size larger than the wavelength of the wave. Only a small diffraction occurs near the corners ofthe obstacle.

The bending or spreading of waves around the ————————————- edges or

corners of ——————- ——————- is called ————————————-

EXAMPLE:3  A student performs an experiment with waves in water. The student measures the wavelength of a wave to be 10 cm. By using a stopwatch and observing the oscillations Of a floating ball, the student measures a frequency of 2 Hz. If the student starts a wave in one part of a tank of water how long will it take the wave to reach the opposite side of the

tank 2 m away?











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