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#condition

3 public questions tagged with this topic.

Forced Oscillations and Resonance

For a motion to be simple harmonic, the restoring force must satisfy which condition when plotted against displacement?

**Forced oscillations** result when external periodic driving force F = F₀ cos(ω_d t) acts on oscillator, steady-state frequency equals driving frequency ω_d, amplitude A = F₀/√((k - m ω_d²)² + (b ω_d)²) depends on proximity to natural frequency ω₀ = √(k/m). Resonance when ω_d ≈ ω₀, amplitude maximum. In SHM, the restoring force is proportional to displacement and opposite in direction ( F = -kx ). When plotted, this yields a straight line through the origin with a negative slope. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result It forms

Ref: NCERT > Physics Book > Oscillations > Forced Oscillations and Resonance

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Moment of Inertia and Radius of Gyration

For a rigid body to be in rotational equilibrium, what condition must be satisfied?

For rotational equilibrium, the net torque about any point must be zero (∑τ = 0), meaning no angular acceleration occurs. As per NCERT, applying relevant law/formula with correct units and sign convention leads to The net torque must be zero. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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