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#uniform circular motion

25 public questions tagged with this topic.

Damped Oscillations

Which statement correctly describes the relationship between SHM and uniform circular motion?

**Damped oscillations** occur when resistive forces dissipate energy, amplitude decays exponentially as A(t) = A₀ e^(-b t/2m), b damping coefficient (kg/s), frequency slightly reduced ω' = √(ω₀² - (b/2m)²). Damping arises from friction or viscosity, energy loss per cycle proportional to velocity squared, motion eventually stops. SHM is the one-dimensional projection of uniform circular motion along a diameter, with the same period but different force characteristics (linear vs. centripetal). Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result SHM is the projection of uniform circular motion on a diameter follows, reflecting

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

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Energy in SHM - Kinetic, Potential and Total

What distinguishes the energy transformation in SHM from that in uniform circular motion?

**Energy distribution** shows maximum kinetic at equilibrium and maximum potential at extremes, sum constant. This relation enables calculation of amplitude, velocity at any displacement via v = ±√(2(E-U)/m), and understanding of energy storage in oscillating system for NEET problems. In SHM, energy oscillates between kinetic and potential forms, while in uniform circular motion, kinetic energy remains constant due to constant speed. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result SHM cycles between kinetic and potential energy follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Energy in SHM - Kinetic, Potential and Total

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Periodic Motion and SHM Basic Concepts

What distinguishes the restoring force in SHM from that in uniform circular motion?

**Periodic motion** repeats after fixed period T, x(t+T)=x(t), while oscillatory motion involves to-and-fro about equilibrium. SHM is special periodic motion where restoring force proportional to displacement, F = -k x, acceleration a = -ω² x, leading to sinusoidal displacement x = A cos(ωt + φ). In SHM, the restoring force is linear ( F = -kx ), varying with displacement, while in uniform circular motion, the centripetal force is constant in magnitude and radial. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result It is linear with respect to displacement follows,

Ref: NCERT > Physics Book > Oscillations > Periodic Motion and SHM Basic Concepts

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