Physics · Class 11 Science
Ch 13Oscillations — Class 11 Physics, concept-first.
Look around, and oscillatory motion is everywhere: a pendulum clock ticking away the seconds, a child on a swing going back and forth, a plucked guitar string vibrating, the diaphragm of a loudspeaker moving rapidly in and out, or even the individual atoms of a solid vibrating about their fixed positions in the crystal…
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Frequency And Period
Imagine a child on a swing, going back and forth. Each full cycle — forward, backward, back to the start — takes a certain amount of time. That time is the period.
Most relevant Q&A
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
Look around, and oscillatory motion is everywhere: a pendulum clock ticking away the seconds, a child on a swing going back and forth, a plucked guitar string vibrating, the diaphragm of a loudspeaker…
Periodic Motion: Period, Frequency and Periodic Functions
A motion is called PERIODIC if it repeats itself, identically, after equal intervals of time. The smallest such interval of time after which the motion FIRST repeats -- so that the system returns to e…
Displacement as a Function of Time
To describe an oscillating system quantitatively, physics tracks its DISPLACEMENT -- how far, and in which direction, the oscillating quantity has moved away from its own equilibrium (mean, or rest) p…
Simple Harmonic Motion (S.H.M.) and Its Equation
SIMPLE HARMONIC MOTION is defined as an oscillatory motion in which the restoring force -- the force that always acts to pull the system back towards its mean (equilibrium) position -- is directly pro…
Phase in Simple Harmonic Motion
The quantity appearing inside the cosine (or sine) function of an S.H.M. is called the PHASE of the oscillation at time .
Velocity and Acceleration in S.H.M.
The velocity and acceleration of a particle executing S.H.M. are found directly by differentiating the displacement with respect to time -- once to get velocity, and a second time to get acceleration:…
Oscillation of a Spring: Restoring Force and Force Constant
A block attached to one end of a spring, with the other end fixed, and free to slide on a frictionless horizontal surface, is the simplest and most direct physical realisation of S.H.M.
Combination of Springs: Series and Parallel
When two (or more) springs act together to support a single oscillating block, the whole combination behaves exactly like ONE single equivalent spring, with some effective, combined force constant tha…
Energy in S.H.M.: Kinetic and Potential Energy
A particle executing S.H.M. continuously exchanges energy between two different forms as it oscillates back and forth: KINETIC energy, associated with its motion, and POTENTIAL energy, stored in the r…
The Simple Pendulum
A SIMPLE PENDULUM consists of a small, heavy bob of mass -- idealised as a single point mass, with all its mass concentrated at one point -- suspended by a light string (treated as perfectly massless)…
The Loaded Spring: Time Period
A "LOADED SPRING" refers to a spring of force constant hung vertically from a fixed support, with a block of mass attached at its lower, free end, so that the block is free to oscillate up and down un…
Free, Damped and Forced Oscillations; Resonance
So far, this whole chapter has treated S.H.M. as continuing forever, unchanged, with a constant amplitude that never dies away.
Summary
Periodic motion: motion repeating after a fixed time (the period); frequency (Hz); angular frequency (rad/s).
Sample & Board Papers
Sample papers and previous-year board questions for this subject.
+−Show 2 questionsHide questions2 questions
More questions
25 Q+−Show 8 questionsHide questions8 questions
- Example 1What is periodic motion? Give two examples of periodic motion from everyday life. Define the period and the frequency of a periodic motion,…Free
- Example 2Show that $x(t) = A\sin(\omega t + \phi)$ is a periodic function of time, and find its period in terms of the angular frequency $\omega$.Free
- Example 3The displacement of a particle executing S.H.M. is given by $x(t) = 6\cos\!\left(4t + \dfrac{\pi}{3}\right)\ \text{cm}$, with $t$ in seconds…Free
- Example 4A spring stretches by $2\ \text{cm}$ when a force of $8\ \text{N}$ is applied to it. Find the force constant of the spring, and write the re…Preview
- Example 5Two springs of force constants $k_1 = 200\ \text{N/m}$ and $k_2 = 300\ \text{N/m}$ are connected (a) in series and (b) in parallel, and supp…Preview
- Example 6A particle of mass $0.2\ \text{kg}$ executes S.H.M. with angular frequency $\omega = 10\ \text{rad/s}$ and amplitude $A = 0.05\ \text{m}$. F…Preview
- Example 7Find the time period of a simple pendulum of length $L = 1\ \text{m}$ at a place where $g = 9.8\ \text{m/s}^2$.Preview
- Example 8A block of mass $0.25\ \text{kg}$ is attached to a spring of force constant $k = 100\ \text{N/m}$ and set into oscillation on a frictionless…Preview
+−Show 9 questionsHide questions9 questions
- Q9Define a periodic function mathematically. Are all periodic functions examples of simple harmonic motion? Justify your answer with an exampl…Free
- Q10Starting from Hooke's law for the restoring force of a spring, $F = -kx$, derive the differential equation of motion for a particle executin…Free
- Q11Explain what is meant by the phase and the phase constant of a particle executing S.H.M. Two particles execute S.H.M. of the same amplitude…Free
- Q12Two springs of force constants $k_1$ and $k_2$ are joined end to end (in series) and support a block. Derive an expression for the equivalen…Preview
- Q13Two springs of force constants $k_1$ and $k_2$ are connected side by side (in parallel) and support a block. Derive an expression for the eq…Preview
- Q14Show, starting from the expressions for kinetic and potential energy of a particle executing S.H.M., that its total mechanical energy remain…Preview
- Q15Derive the expression for the time period of a simple pendulum, $T = 2\pi\sqrt{L/g}$, starting from the restoring torque acting on the bob.…Preview
- Q16Distinguish between free oscillations, damped oscillations and forced oscillations, giving one example of each.Preview
- Q17What is resonance? Explain, in qualitative terms, why the amplitude of a forced oscillation becomes very large when the driving frequency is…Preview
+−Show 8 questionsHide questions8 questions
- Q18A particle executes S.H.M. with amplitude $5\ \text{cm}$ and period $2\ \text{s}$. Find its maximum velocity and maximum acceleration.Free
- Q19The displacement of a particle in S.H.M. is $x = 4\sin\!\left(5t + \dfrac{\pi}{6}\right)\ \text{cm}$, with $t$ in seconds. Find the amplitud…Free
- Q20A body of mass $0.5\ \text{kg}$ attached to a spring executes S.H.M. with a time period of $0.6\ \text{s}$. Find the force constant of the s…Free
- Q21Two springs of force constants $100\ \text{N/m}$ and $150\ \text{N/m}$ are connected in series. Find the equivalent force constant of the co…Preview
- Q22The same two springs of Numerical 4 ($100\ \text{N/m}$ and $150\ \text{N/m}$) are instead connected in parallel and support a block of mass…Preview
- Q23A particle of mass $0.1\ \text{kg}$ executing S.H.M. has a total energy of $8 \times 10^{-3}\ \text{J}$ and an amplitude of $0.1\ \text{m}$.…Preview
- Q24Find the length of a simple pendulum whose time period is $2\ \text{s}$ at a place where $g = 9.8\ \text{m/s}^2$.Preview
- Q25A body of mass $1\ \text{kg}$ is suspended from a spring of force constant $400\ \text{N/m}$ and set into vertical oscillation. Find (a) the…Preview