The Physics Of Oscillation: The Basics Physics – Cha 7 (Oscillation)
Oscillation is defined as the process of repeating variations of any quantity or measure about its equilibrium value in time.
What is oscillation?
Oscillation involves the coincidence of phases of something with other phases. Oscillation comes in three major patterns. A sine wave is a repeating pattern in which there are periodic waves with peaks and valleys. A sine wave can be generated by moving a pendulum on a swing arm. A square wave is a repeating pattern in which the square wave of one oscillation (say the sine wave) repeats inside the square wave of the following oscillation. A sawtooth wave is a repeating pattern in which the wavelength of the sine wave or sawtooth wave oscillates within a very small, narrow range. We use oscillation patterns to visualize complex real-life phenomena such as the wavefronts in the ocean, the pulsing of the heart, the diurnal motion of plants, and the variations of the movement of waves.
Types of oscillation
The 4 main types of oscillations are amplitude, frequency, power, and phase. An amplitude oscillation is when an energy source (such as electricity or sound waves) is added to a quantity of material. As the energy source adds it to the material the resulting pattern of variation becomes stretched out. In the case of material being stretched, the duration of this change (the amplitude) is measured in cycles (a cycle is a one-time step in the cycle). A frequency oscillation is when an energy source (such as electricity or sound waves) is added to a quantity of material. As the energy source adds it to the material the resulting pattern of variation becomes stretched out. In the case of material being stretched, the frequency (the time taken for a cycle to complete) is measured in Hz.
You can do the following (slightly simplified) experiment: You can place a bell in a bottle and shake it from side to side. While it is still spinning, put it down and remove it from the bottle. Now you can shake it violently from the bottom of the bottle until it stops, but it will not ring. If you shake it gently from the top of the bottle until it stops, it will keep ringing. There is something called the Bohr effect that causes a change in the properties of a molecule when it interacts with magnetic fields. That means that a magnet placed in a bottle will make the molecules inside the bottle “spin.” You could play this on a string by placing a coin on the string and shaking it. It will remain fixed and won’t drop (or make a sound) when you shake the coin.
Conceptual Questions Chapter 7 (Oscillation) class 11
Q.1) Give two applications in which resonance plays an important role.
1. Radio and Resonance:
Tuning a radio is the best example of electrical resonance. When we have to listen to a specific station, we turn the knob at different points. By turning the knob, we change the natural frequency of the electric circuit of the receiver. We do this in order to make the natural frequency equal to the transmission frequency of the radio station. And when the two frequencies match then the energy absorption will be maximum so in that way we only listen to a specific radio.
2. Magnetic Resonance Image (M.R.I):
Another example of resonance is magnetic resonance scanning. It has greatly enhanced medical diagnoses.
In this technique, strong radiofrequency radiations are used to cause nuclei of atoms to oscillate. At the point when resonance occurs, the energy is absorbed by the molecules. This pattern of energy absorption is then used to produce a computer-enhanced photograph that gives us detail information about the scanned area.\
Q.4) Give one practical example each of free and forced oscillation.
“A body is said to be executing free vibrations or free oscillations if it oscillates with its natural frequency without the interference of an external force”.
For example, a simple pendulum vibrates freely with its natural frequency and is not under the influence of any external force. Its natural frequency depends only upon its length when it is slightly displaced from its mean position.
“If a freely oscillating system is subjected to an external force, then forced vibrations will take place and these oscillations is known as forced oscillations”
For example, when the mass of the pendulum is struck repeatedly, then forced vibrations are produced.
Another example is the vibration of the factory floor. When heavy machinery runs in a factory, this causes little vibration on the floor of the factory.
The production of loud music due to the sounding wooden boards of strings instrument is also an example of forced oscillations.
Q.8) What is the total distance covered by a simple harmonic oscillator in a time equal to its period? The amplitude of oscillation is A.
The time period is defined as the time required to complete one vibration. Thus in one vibration, the oscillator moves from one extreme position say ‘B’ towards a mean position say ‘O’, continues its moved to the other extreme position say ‘C’ and then returns back to the first extreme position ‘B’ after passing through the mean position ‘O’. The distance from mean position to extreme position i.e. amplitude OB = OC = A so the total distance covered in one vibration is;
BO+ OC+ CO+ OB= A + A + A + A = 4A
Q.10) A singer, holding a note of right frequency, can shatter a glass. Explain.
Yes, a singer holding right note of frequency can shatter a glass. This happens as a result of resonance.
As every solid body can vibrate at a certain frequency and if the singer holds a particular frequency in his singing equal to the natural frequency of the glass, then resonance occurs. Therefore, the amplitude of vibrations of the glass atoms will go on the increase. As a result, the glass will shatter.
Comprehensive Questions class 11 physics notes
Q.1) Show that motion of a mass attached with a spring executes S.H.M
Simple harmonic motion (S.H.M) is the type of motion in which the acceleration is always directly proportional to the displacement of the body to the mean position, and is always directed toward the mean position.
Now if we take a mass “m” and attach it to a spring of spring constant “k”. Initially when the spring is at rest the position of the mass is denoted by “O” called mean position. We stretch the spring and displace the mass, by applying some force, to a new position “A” as shown in figure.
The spring will exert the same amount of force in the opposite direction on the mass called restoring force and is given as,
F = – kx
Then if we release the body it will move toward the mean position “O” and reach to a new position “B” on the other side of “O” due to inertia. At point B the spring is compressed so it again apply force on the mass and push it back toward mean position and in this manner the body start oscillation between point A and B.
Mathematically we can explain it as,
At point A:
Fapplied = – Frestoring
According to Hook’s law,
kx = -Frestoring
On comparing with Newton’s second law of motion;
kx = -ma
a = – (k/m)x
During the motion, ‘k’ and ‘m’ remain constant. Then,
a = constant (-x)
a ∝ -x
The spring constant ‘k’ depends upon the nature of spring i.e. on its shape and structure. Also from the above relation it can be seen that ‘a’ is directly proportional to ‘x’ and directed towards mean position. So that’s why we can say the motion of a mass attached to a spring execute simple harmonic motion.
Q.2) Prove that the projection of a body motion in a circle describes S.H.M.
Let a body move in a vertical circle with radius ‘r’ and diameter AB.
When the body move in a circle the projection ‘Q’ of the body moves along the diameter, when the body completes one rotation its projection also reach to the same point on the diameter of circle from where it starts moving. If the body is at point ‘P’ as it is shown in the figure, its projection ‘Q’ is at distance ‘x’ from the mean position ‘O’. If ac is the centripetal acceleration of the body which is always directed towards the center of the circle i.e. toward the mean position ‘O’, we can write the x and y components of ac as follows.
ax= rω2(x/r) = xω2
As we know that ax is a component of centripetal acceleration so it will always be directed toward the center of the circle that’s why we can write;
ax = ω2(-x)
where the negative sign shows the direction. As the body is rotating with a constant angular velocity. So we can write as,
ax = constant (-x)
a ∝ -x
Which is the equation of S.H.M. so we proved that the projection of a body shows simple harmonic motion.
Q.3) Show that energy is conserved in case of S.H.M.
Consider a SHM such as mass ‘m’ suspended from a strong support by means of a spring of spring constant ‘k’ as shown in figure.
Let the mass is pulled through the displacement xo and released. The mass will oscillate with amplitude xo. Let at the certain instant of time the oscillating mass is at displacement x from the equilibrium position O. According to hook’s law the applied force is directly proportional to the displacement x. Now the K.E and P.E can be derived as follow;
Kinetic Energy in a Simple Harmonic Motion:
As the K.E of a simple harmonic oscillator moving with an instantaneous velocity is;
K.E = 1/2 mv2 ………….. (i)
v = ω√ (xo2 – x2)
Substituting value of v in eq (i)
Thus the K.E will be maximum at the mean position i.e. when x = 0
The Kinetic energy will be minimum (zero) a extreme position i.e. when x = xo
Potential Energy in Simple Harmonic Motion:
Initially when the spring/ body is in equilibrium at point ‘O’ the net force acting on the body is
Fi = 0.
If we apply a force F = mω2x, it covers the displacement x. So, according to the Hook’s law if the displacement is ‘xo’, then the force
Ff = mω2xo = kxo
So the average force acting on mass during displacement x is;
The P.E is maximum when the oscillator is at extreme position i.e. x = xo
P.Emax = 1/2 kxo2
The P.E is minimun when the oscillator is at mean position i.e. x = 0
P.Emin =1/2 k(0) = 0
Total Energy of SHM:
As the energy of a simple harmonic oscillator at a displacement x is partly kinetic and partly potential. The total kinetic energy at x is;
T.E = K.E + P.E
Substituting values of K.E and P.E
Thus the T.E of SHM always remains constant. At mean position P.E is zero and the whole energy is K.E. At extreme position K.E is zero and the whole energy is P.E. The energy oscillates back and forth between K.E and P.E but the T.E remains conserved.
Q.4) Differentiate free and forced oscillations.
“It is the motion of a body about an equilibrium position, also called mean position/ mean point”.
There are two types of oscillations, named as free oscillation and forced oscillation.
It is the type of oscillation in which the oscillating body oscillates with its natural frequency, without the interference of an external force.
It is the type of oscillation in which some amount of external force is supplied to the oscillating body.
Example of Free Oscillations:
For example, A simple pendulum vibrating with its natural frequency. It only depends upon its length when it is displaced from the mean position.
Example of Forced Oscillations:
For example, if we consider again a simple pendulum but we move the bob of the simple pendulum to a new position and after the release when it starts oscillation, we repeatedly strike the bob and supply some external force to the pendulum. In this case the oscillation executed by sample pendulum is known as forced oscillation.
Another example of forced oscillation is loud music produced by sounding wooden boards of strings instruments. The vibrations of a factory floor caused by the running of heavy machinery are also an example of forced vibration.
Q.5) What is resonance give three of its applications in our daily life.
“When the externally applied frequency becomes equal to the natural frequency of an oscillating body, it starts motion with greater amplitude then the body is said to be in resonance.”
There are many applications of resonance in our daily life, three of them are explained below one by one.
A microwave oven uses frequency similar to the natural frequency of the water and fat molecules. So, when we place some food in a microwave oven, the waves fall upon it. As the waves are of similar frequency to that of water so it resonates the water molecule or fat molecule only, and absorb the energy from the microwaves. Due to this reason only those thing heats up in the oven which has water molecules or fat molecules.
Radio and Resonance:
Radio is the best example of resonance. When we turn the knob of our radio to set a channel, it means we are changing the natural frequency of our receiver (radio). When the frequency of the receiver becomes similar to the frequency of transmission frequency of a radio station, the resonance occurs and the maximum amount of energy absorbs. Thus we listen to this station only.
Magnetic Resonance image (M.R.I):
This is the application of resonance in the medical field. Due to M.R.I diagnosis is now much improved than before. In a magnetic resonance imaging technique, the nuclei of atoms are resonated with the help of strong radio waves. Different nuclei resonate at different frequencies, therefore, they absorb different energies. So, they form a specific pattern of energy absorption and that pattern is used by a computer to produce a computer-enhanced photograph which we call M.R.I
Q.7) Explain what is mean by damped oscillations.
Oscillations are said to be damped if they are changed by some opposing forces. Ideally the total energy of oscillation remains constant. It is conserved in all oscillations like in mass attached to a spring, body moving in circular motion and also in case of simple pendulum, according to which if we disturb an oscillating body from its equilibrium, it will remain in oscillation until we stop it, but in real it is not so. All oscillating objects stop oscillation after some time due to frictional forces. So, oscillation does die out with the time until energy is continuously supplied to the body. For example, in case of swing, to keep the swing in continuous oscillation we must push it continuously in a specific direction and at a specific time. So we can say that
“The oscillation in which the amplitude of oscillation become smaller and smaller with the time is called damped oscillation”.
The damping of oscillation is also very useful phenomena, the concept of damping is used in the shock absorbers i.e. in the suspension system of our cars and motorcycle etc. which provide us with a comfortable ride even on rough and bumpy surfaces.