Oscillations
Maharashtra Board · Class 12 · Physics
Practice quiz for Oscillations — Maharashtra Board Class 12 Physics. MCQs and questions with answers to test your preparation.
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Quick Quiz: Oscillations
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A particle performs S.H.M. with amplitude 4 cm and time period 2 s. What is the maximum velocity of the particle?
A spring-mass system has force constant k = 100 N/m and mass m = 0.25 kg. What is the period of oscillation?
A simple pendulum of length 1 m oscillates on Earth where g = 10 m/s². What is its time period?
The differential equation of S.H.M. is d²x/dt² + ω²x = 0. What does ω represent?
Sample Questions
Which of the following conditions are necessary for Simple Harmonic Motion?
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Restoring force is proportional to displacement, Restoring force is directed towards mean position, Motion is periodic, Motion occurs about a fixed point
For S.H.M.: (1) Force ∝ -displacement (2) Force directed towards equilibrium (3) Motion is periodic (4) Motion about fixed point. Amplitude can change in damped oscillations.
In S.H.M., when displacement is maximum, which physical quantities are zero?
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Velocity, Kinetic energy
At extreme positions (maximum displacement): velocity = 0, hence kinetic energy = 0. Potential energy is maximum, acceleration is maximum (directed toward center), total energy remains constant.
A particle in S.H.M. has maximum kinetic energy 20 J and amplitude 0.1 m. If mass is 2 kg, find the angular frequency ω.
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10 rad/s
Maximum kinetic energy = ½mω²A². Given: KE_max = 20 J, m = 2 kg, A = 0.1 m. So: 20 = ½ × 2 × ω² × (0.1)² = ω² × 0.01. Therefore: ω² = 20/0.01 = 2000, ω = √2000 = 10√20 ≈ 10 rad/s
Which factors affect the time period of a simple pendulum?
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Length of pendulum, Acceleration due to gravity
From T = 2π√(L/g), time period depends only on length L and gravity g. It's independent of mass, amplitude (for small angles), and string material.
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