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NCERT Solutions for Class 11 Physics Ch-13: Oscillations
NCERT Solutions for Class 11 Physics Chapter 13 Oscillations covers periodic and simple harmonic motion (SHM), the characteristics of SHM such as displacement, velocity and acceleration, energy in SHM, and the simple pendulum.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: Define simple harmonic motion (SHM).
Answer: Simple harmonic motion is a type of periodic motion in which the restoring force (or acceleration) acting on a particle is always directed towards a fixed equilibrium point and is directly proportional to the displacement of the particle from that point, mathematically expressed as F = −kx.
Q2: Write the expressions for displacement, velocity, and acceleration of a particle executing SHM.
Answer: For a particle in SHM, displacement is x = A sin(ωt + φ), velocity is v = Aω cos(ωt + φ), and acceleration is a = −Aω² sin(ωt + φ) = −ω²x, where A is the amplitude, ω is the angular frequency, and φ is the phase constant.
Q3: How does the total mechanical energy of a particle in SHM vary with time?
Answer: The total mechanical energy of a particle executing SHM (sum of kinetic and potential energy) remains constant at all times, equal to (1/2)kA² = (1/2)mω²A², even though kinetic and potential energy individually vary and interconvert continuously as the particle oscillates.
Q4: Derive the expression for the time period of a simple pendulum.
Answer: For a simple pendulum of length L undergoing small-angle oscillations, the restoring force leads to SHM with angular frequency ω = √(g/L), giving a time period T = 2π√(L/g), where g is the acceleration due to gravity.
Q5: What is the time period of oscillation of a mass-spring system?
Answer: For a mass m attached to a spring of spring constant k undergoing SHM, the time period is given by T = 2π√(m/k), independent of the amplitude of oscillation.
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