# Class 11 Physics Oscillations: NCERT Solutions for Question 16

This page focuses on the detailed Oscillations question answers for Class 11 Physics Oscillations, addressing the question: '( i ) The time period of a body having simple harmonic motion depends on the mass m of the body and the force constant k: T =2π √m/k A simple pendulum exhibits simple harmonic motion. Then why does the time period of a pendulum not depend upon its mass? ( ii ) For small angle oscillations, a simple pendulum exhibits simple harmonic motion ( more or less). For larger angles of oscillation, detailed analysis show that T is greater than 2π√ l/g. Explain. ( iii ) A boy with a wristwatch on his hand jumps from a helicopter. Will the wrist watch give the correct time during free fall? ( iv ) Find the frequency of oscillation of a simple pendulum that is free falling from a tall bridge.'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 16

## ( i ) The time period of a body having simple harmonic motion depends on the mass m of the body and the force constant k:T =2π √m/kA simple pendulum exhibits simple harmonic motion. Then why does the time period of a pendulum not depend upon its mass?( ii ) For small angle oscillations, a simple pendulum exhibits simple harmonic motion ( more or less). For larger angles of oscillation, detailed analysis show that T is greater than 2π√ l/g. Explain.( iii ) A boy with a wristwatch on his hand jumps from a helicopter. Will the wrist watch give the correct time during free fall?( iv ) Find the frequency of oscillation of a simple pendulum that is free falling from a tall bridge.

( i ) The time period of a simple pendulum, T =2π √m/k  For a simple pendulum, k is expressed in terms of mass m, as:

k ∝ m

m/k = constant

Thus, the time period T, of a simple pendulum is independent of its mass.

( ii ) In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is:

F = –mg sinθ

Where, F = Restoring force

m = Mass of the bob

g = Acceleration due to gravity

θ = Angle of displacement

For small θ, sin θ ∼ θ

For large θ, sin θ is greater than θ. This decreases the effective value of g.

Thus, the time period increases as: T = 2π√ l/g'

( iii ) As the working of a wrist watch does not depend upon the acceleration due to gravity, the time shown by it will be correct during free fall.

( iv ) As acceleration due to gravity is zero during free fall, the frequency of oscillation will also be zero.