Chapter 13: Oscillations Short Questions | physics Class 11 CBSE

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Chapter 13: Oscillations Short Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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Define periodic motion and give two examples from daily life mentioned in the chapter.

Periodic motion is a motion that repeats itself at regular intervals of time.
Example 1: The oscillation of the pendulum of a wall clock, which moves to and fro about a mean position.
Example 2: A boat tossing up and down in a river, repeating its motion periodically.

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Question 2

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Distinguish between oscillatory motion and periodic motion with one example of each.

Periodic motion is any motion that repeats at regular time intervals; oscillatory motion is a special type where the body moves to and fro about a mean equilibrium position.
Every oscillatory motion is periodic, but every periodic motion need not be oscillatory — for example, circular motion is periodic but not oscillatory.
Example of oscillatory motion: a swinging pendulum. Example of periodic but non-oscillatory motion: the orbital motion of a planet.

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Question 3

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State the relationship between period T and frequency ν of a periodic motion, and give the SI unit of frequency.

The relationship between period and frequency is ν = 1/T, meaning frequency is the reciprocal of the time period.
The SI unit of frequency is hertz (Hz), named after Heinrich Rudolph Hertz.
One hertz equals one oscillation per second, i.e., 1 Hz = 1 s⁻¹.

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Question 4

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Write the standard equation for displacement in SHM and identify each symbol used.

The displacement equation for SHM is x(t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, φ is the phase constant, and (ωt + φ) is the phase.
The amplitude A is the magnitude of the maximum displacement of the particle from the equilibrium position.
The phase constant φ represents the initial phase at t = 0 and is determined by the initial conditions of the motion.

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Question 5

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What is the phase constant in SHM, and what determines its value?

The phase constant φ is the value of the phase (ωt + φ) at t = 0, representing the initial state of the oscillating particle.
Its value is determined by the initial conditions: if the amplitude A is known, φ can be found from the displacement at t = 0.
Two SHMs may have the same amplitude A and angular frequency ω but different phase constants φ, resulting in different states of motion at t = 0.

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Question 6

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Write the expressions for velocity and acceleration of a particle executing SHM and state their amplitudes.

The velocity of a particle in SHM is v(t) = −ωA sin(ωt + φ), with velocity amplitude ωA.
The acceleration is a(t) = −ω²A cos(ωt + φ) = −ω²x(t), with acceleration amplitude ω²A.
Both velocity and acceleration are periodic functions of time with the same period T as displacement.

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Question 7

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State the force law for simple harmonic motion and define the force constant k.

The force law for SHM is F(t) = −kx(t), where the force is always directed towards the mean position (restoring force).
The force constant k = mω², where m is the mass of the particle and ω is the angular frequency.
Since force is proportional to displacement, the angular frequency is related to the force constant by ω = √(k/m).

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Question 8

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What is a linear harmonic oscillator? How does it differ from a non-linear oscillator?

A linear harmonic oscillator is a particle oscillating under a restoring force that is linearly proportional to displacement: F = −kx.
In a non-linear oscillator, the force contains additional terms proportional to x², x³, etc., making the restoring force non-linear in displacement.
Real-world systems approximate linear harmonic oscillators for small displacements but may show non-linear behaviour at larger amplitudes.

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Question 9

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Write the expressions for kinetic and potential energy of a particle in SHM and state when each is maximum.

Kinetic energy K = ½kA² sin²(ωt + φ); it is maximum (= ½kA²) when displacement x = 0, i.e., at the mean position.
Potential energy U = ½kA² cos²(ωt + φ); it is maximum (= ½kA²) when displacement x = ±A, i.e., at the extreme positions.
Both K and U are always non-negative and vary periodically with period T/2, half the period of the oscillation.

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Question 10

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State the expression for total mechanical energy in SHM and comment on its time dependence.

The total mechanical energy in SHM is E = K + U = ½kA², where k is the force constant and A is the amplitude.
The total energy is independent of time and remains constant throughout the oscillation, as the spring force is conservative.
Energy continuously exchanges between kinetic and potential forms, but their sum always equals ½kA².

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Question 11

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Derive the period of a simple pendulum from its equation of motion for small angles.

For small angular displacement θ, sin θ ≈ θ, so the restoring torque gives α = −(mgL/I)θ, which has the form of SHM.
Comparing with α = −ω²θ, we get ω = √(mgL/I). Since the string is massless, I = mL², giving ω = √(g/L).
The period is therefore T = 2π/ω = 2π√(L/g), which is independent of the mass of the bob.

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Question 12

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How is SHM related to uniform circular motion? What is the reference circle?

SHM is the projection of uniform circular motion on a diameter of the reference circle; if particle P moves uniformly on a circle, its projection P′ executes SHM.
The reference circle is a circle of radius equal to the amplitude A, on which the reference particle moves uniformly with the same angular frequency ω as the SHM.
The projection on the x-axis gives x(t) = A cos(ωt + φ), while the projection on the y-axis gives y(t) = A sin(ωt + φ), with a phase difference of π/2.

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Question 13

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What is the phase difference between displacement, velocity, and acceleration in SHM?

Velocity leads displacement by a phase of π/2 (quarter period), as v(t) = −ωA sin(ωt + φ) while x(t) = A cos(ωt + φ).
Acceleration leads displacement by a phase of π (half period), as a(t) = −ω²A cos(ωt + φ) = −ω²x(t).
All three quantities — displacement, velocity, and acceleration — have the same period T but differ in phase.

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Chapter sections

Chapter 13: Oscillations | Short Questions

Define periodic motion and give two examples from daily life mentioned in the chapter.

Distinguish between oscillatory motion and periodic motion with one example of each.

State the relationship between period T and frequency ν of a periodic motion, and give the SI unit of frequency.

Write the standard equation for displacement in SHM and identify each symbol used.

What is the phase constant in SHM, and what determines its value?

Write the expressions for velocity and acceleration of a particle executing SHM and state their amplitudes.

State the force law for simple harmonic motion and define the force constant k.

What is a linear harmonic oscillator? How does it differ from a non-linear oscillator?

Write the expressions for kinetic and potential energy of a particle in SHM and state when each is maximum.

State the expression for total mechanical energy in SHM and comment on its time dependence.

Derive the period of a simple pendulum from its equation of motion for small angles.

How is SHM related to uniform circular motion? What is the reference circle?

What is the phase difference between displacement, velocity, and acceleration in SHM?

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