Isn’t it interesting how simple to and fro motion of a pendulum can be classified into so many different forms, giving rise to some of the essential concepts for the Physics syllabus for class 11? You must have studied this concept in Science textbooks of class 8 – 10th as well. But class 11 Physics includes a more complex version of the theory. It is also asked in competitive exams like JEE Mains and JEE Advanced. Here are some to the point notes on class 11 Oscillations.
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What are Oscillations?
In physics, oscillation stands for regular variation in magnitude or position about a central point, especially of an electric current or voltage. In simple terms, it is the movement back and forth in a regular rhythm. For Example, in a swing, pendulum of a clock, etc.
Types of Motions
As the object that oscillates is in motion, let us have a look at what are the different types of motions in oscillations. There are primarily three types of motions that are covered under the class 11 oscillations chapter that students must be familiar with-
A motion that repeats itself periodically. For Example: the hands of the clock.
A motion which goes to and fro, and back, instead of full-motion. For Example: the clock’s pendulum.
Simple Harmonic Motion (SHM)
It is the type of motion in which the particle oscillates back ad forth in a straight line only. For Example: Bungee Jumping.
Before we move on to the next part of class 11 oscillations notes,
go through our blog on Laws of Motion Class 11.
Let us take a deeper look at different types of motion
A periodically repeating motion is a function of time. The two values concerning the periodic motions are T (time period) and v (frequency). Time Period refers to the time period after which the motion repeats itself. The frequency is the number of repetitions per unit of time (v = 1/T).
For Example: The hour’s clock repeats itself every 12 hours. The time period here is 12 hours, and the frequency is 1/12 per hour. Similarly, for a minute’s hand, the T = 1 hour, and the v = 1 per hour. For second’s hand, the T = 1 minute or 1/60 hour, and v = 1/T = 60 per hour.
Oscillatory Motions are those that go to and fro, and then back. Oscillatory motions can be seen in both non- periodic and periodic motion. They can also have fixed extreme positions, but there is no rule for such fixed positions either. Oscillatory motions are operated upon a restoring force or torque that directs the motion towards the equilibrium position.
Simple Harmonic Motion (SHM)
Simple Harmonic Motions are those forms of oscillations where the restoring force is directly proportional to the displacement from the mean position, thus creating a fixed set of motion called as a simple harmonic motion. It is an important pointer of the class 11 oscillations chapter, hence, should be discussed in detail. Three primary conditions are required for a simple harmonic motion to be possible are-
- A position where there is a stable equilibrium resulting from zero potential energy
- Energy is conserved, i.e., there’s no dissipation of energy
- Acceleration is proportional to the displacement
Equation of Simple Harmonic Motion
As you are through with the theoretical part of the class 11 oscillations chapter, now let us understand the equation as well as the formula of SHM.
F = -ky (b) d2y/dt2 +ω2y = 0
ω = √k/m (k is Force constant)
Displacement (y): At any instant, the displacement of a particle is defined as the distance between the mean position and the particle’s present position.
Amplitude (r): Maximum displacement from the mean position on either side of the motion is Amplitude.
Velocity: In the SHM oscillations, the velocity can be defined as-
V= dy/dt = rωcos(ωt+?)
= vcos(ωt+?) = ω√r2-y2
In the above-mentioned equation, v is the linear velocity of the particle.
Condition: When, y = 0, then, V = v = rω
When, y = ±r, then, V=0
Acceleration: Acceleration in simple harmonic motion oscillations is defined by the following equation:
a = dV/dt = (-v2/r) sinωt = -ω2y
Condition: When, y = 0, then, a = 0 And When, y = ±r, then, a = ±ω2r
Time Period is the time taken to complete one vibration (similar to complete motion in periodic motion)
Frequency is the number of vibrations per second (f)
Angular frequency = ω = 2πf=√k/m
Also Read: Modern Physics
Oscillations: Important Questions
Whether you are preparing for scholastic exams or entrance exams going through the NCERT is very important. You must strive to solve all the questions of the NCERT book as it is rewarding for a student. Some of the common class 11 oscillations chapter questions are-
- Identify the types of motion or which of the following is periodic motion or which of the following is simple harmonic motion etc
- Identify the motion: The ones having simple harmonic motion, and ones which are periodic but not simple harmonic motion
- Among the given functions of time which are the ones representing: (i) simple harmonic, (ii) periodic but not simple harmonic motion, and (iii) non-periodic motion
- Find the period for each case of periodic motion (ω is a positive constant):
a) sin ωt – cos ωt
c) 3 cos (π/4 – 2ωt)
d) cos ωt + cos 3ωt + cos 5ωt
e) exp (–ω2 t2 )
f) 1 + ωt + ω2 t2
Exercise Based on Textbook
Q1. Which of the following represents periodic motion?
- A swimmer completing one (return) trip from one bank of a river to another and back.
- A freely suspended bar magnet displaced from its N-S direction and released.
- A hydrogen molecule rotating about its center of mass.
- An arrow is released from a bow.
Sol: (a) The swimmers’ motion is not period and this is because the time taken by the swimmer may not be the same during his back and forth journey.
(b) A suspended bar magnet have a definite period of time when it oscillates from N-S, so it is periodic.
(c) This is periodic because when a hydrogen molecule rotates about its center of mass, it comes to a similar position again and again after an equal interval of time.
(d) This is definitely not periodic because when an arrow gets released it only moves in the forward direction and does not come back forward.
Q2. Which of the following examples represents (nearly) simple harmonic motion and which represents periodic but not simple harmonic motion?
- The rotation of the earth about its axis
- Motion of an oscillating mercury column in a U-tube.
- Motion of a ball-bearing inside a smooth curved bowl, when released from a point slightly above the lowermost point.
- General vibrations of a polyatomic molecule about its equilibrium position.
Sol: (a) It is period but not S.H.M because the rotation of the earth is not to and fro motion about a fixed point.
(b) Simple harmonic motion
(c) Simple harmonic motion
(d) It is periodic but not S.H.M
Q3. Fig. 14.23 depicts four x-t plots for the linear motion of a particle. Which of these plots represent periodic motion? What is the period of motion (in case of periodic motion)?
Sol: (a) It is not periodic motion because the motion does not repeat itself after a regular interval of time.
(b) It is a periodic motion, which is repeating itself after 2 seconds.
(c) It is not a periodic motion because the motion is being repeated in one position only.
(d) It is a periodic motion, which is repeating itself after 2 seconds.
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