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#restoring force

11 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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Damped Oscillations

What distinguishes the oscillatory nature of a pendulum from the periodic motion of a planet in orbit?

**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. A pendulum oscillates about a fixed point due to a linear restoring force (gravity component), while a planet’s orbit is periodic but governed by inverse-square gravitational force. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result The restoring force is linear follows, reflecting SHM dependence

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

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Equations of SHM, Phase and Angular Frequency

What fundamental property of the restoring force distinguishes simple harmonic motion from other oscillatory motions?

**General equation of SHM** x = A sin(ωt + φ) or A cos(ωt + φ) includes amplitude A (m), angular frequency ω = √(k/m) (rad/s) for spring system, and initial phase φ (rad) setting t=0 position. Phase (ωt + φ) determines instantaneous state, phase difference Δφ governs interference of two SHM motions. In SHM, the restoring force must be directly proportional to displacement and opposite in direction ( F = -kx ), ensuring a linear relationship, unlike non-linear oscillatory systems. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result Its linearity

Ref: NCERT > Physics Book > Oscillations > Equations of SHM, Phase and Angular Frequency

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Energy in SHM - Kinetic, Potential and Total

Which periodic motion lacks a restoring force directed towards a fixed equilibrium point?

**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. The rotation of a carousel is periodic but not oscillatory, as it involves continuous circular motion without a restoring force towards a fixed point, unlike SHM systems. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result The rotation of a carousel 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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Simple Pendulum and Angular SHM

What is a key reason the simple pendulum deviates from SHM at large angular displacements?

**Angular SHM** of pendulum results from restoring torque τ = -m g L sinθ ≈ -m g L θ for small θ, analogous to linear SHM with ω = √(g/L). This relation allows period determination from length and local gravity, illustrating gravitational influence on oscillation. At large angles, the sinusoidal restoring torque ( tau = -mgL sin θ ) introduces non-linear terms, disrupting the linear proportionality required for SHM. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result The restoring torque becomes non-linear follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Simple Pendulum and Angular SHM

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Periodic Motion and SHM Basic Concepts

What causes the restoring force in a spring-mass system to initiate SHM?

**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). The elasticity of the spring generates a restoring force ( F = -kx ) proportional to displacement, driving the oscillatory motion characteristic of SHM. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result Elasticity of the spring follows, reflecting SHM dependence on amplitude A, ω and system parameters.

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

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Spring-Mass System and Combination of Springs

Which factor in a spring-mass system directly influences the stiffness of the restoring force?

**Spring-mass system** has period T = 2π√(m/k), frequency f = (1/2π)√(k/m), ω = √(k/m), where k spring constant (N/m) and m mass (kg). For parallel combination, k_eff = k₁ + k₂, series gives 1/k_eff = 1/k₁ + 1/k₂, affecting ω = √(k_eff/m) and T = 2π√(m/k_eff). The spring constant ( k in F = -kx ) determines the stiffness, as it measures the force per unit displacement, affecting the system’s oscillation characteristics. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result Spring constant follows, reflecting SHM dependence on amplitude A, ω and system parameters.

Ref: NCERT > Physics Book > Oscillations > Spring-Mass System and Combination of Springs

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Energy in SHM - Kinetic, Potential and Total

In SHM, when does the particle experience its maximum restoring force?

**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. The restoring force ( F = -kx ) is maximum at the extreme positions ( x = ± A ), where displacement is greatest, coinciding with maximum potential energy. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result At the extreme positions 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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Simple Pendulum and Angular SHM

What distinguishes the restoring force in a spring-mass system from that in a simple pendulum at small amplitudes?

**Angular SHM** of pendulum results from restoring torque τ = -m g L sinθ ≈ -m g L θ for small θ, analogous to linear SHM with ω = √(g/L). This relation allows period determination from length and local gravity, illustrating gravitational influence on oscillation. The spring-mass system uses elastic force ( F = -kx ), constant with displacement, while the pendulum’s force ( F = -mg sin θ ≈ -mg θ ) derives from gravity and varies with angle. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result It is

Ref: NCERT > Physics Book > Oscillations > Simple Pendulum and Angular SHM

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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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Transverse and Longitudinal Waves

What is the primary source of restoring force for transverse waves on a stretched string?

**Mechanical waves** require medium and can be transverse or longitudinal. Sound in air is longitudinal since fluids support only compressional motion, while string waves are transverse. Progressive waves transfer energy without net mass transport, distinguishing from standing waves. In transverse waves on a string, the tension provides the restoring force that opposes displacement, enabling wave propagation, unlike elasticity or pressure in other contexts. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Tension, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Transverse and Longitudinal Waves

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