The equivalent resistance of two resistors in series is simply the sum of their resistances: R_eq = R1 + R2.

The force on a charged particle moving in a magnetic field is given by F = qvB sin(θ), where θ is the angle between the velocity and the magnetic field.

The fringe separation (β) is given by the formula β = λD/d, where λ is the wavelength, D is the distance to the screen, and d is the distance between the slits.

The fringe width (β) is given by the formula β = λD/d, where D is the distance from the slits to the screen and d is the distance between the slits.

The magnetic field inside a solenoid is given by B = μ₀(nI), where n is the number of turns per unit length.

The magnetic force on a charged particle is given by F = qvBsin(θ), where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.

The magnetic force on a charge moving in a magnetic field is given by F = qvBsinθ, where θ is the angle between v and B.

The magnetic force on a charged particle is given by F = qvBsinθ, where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between v and B.

The modulus of resilience is given by U = 1/2 * σ * ε, where σ is the yield stress and ε is the yield strain.

The total power in a series RLC circuit is given by P = VI cos(φ), where φ is the phase angle.

Young's modulus (E) is defined as the ratio of stress to strain.

Frequency (f) = speed/wavelength = 343 m/s / 0.5 m = 686 Hz.

Frequency (f) = Speed (v) / Wavelength (λ) = 340 m/s / 0.5 m = 680 Hz.

Frequency is the reciprocal of the period. Therefore, frequency = 1/period = 1/0.01 = 100 Hz.

Frequency f is the reciprocal of the period T, given by f = 1/T. Therefore, f = 1/0.02 s = 50 Hz.

Frequency f is the reciprocal of the period T. Therefore, f = 1/T = 1/0.01 s = 100 Hz.

Frequency f = Speed / Wavelength = 340 m/s / 2 m = 170 Hz.

Fringe width β = λD/d = (500 x 10^-9 m)(1 m)/(0.2 x 10^-3 m) = 2.5 mm.

The fundamental frequency is given by f = v/λ. For a pipe open at both ends, λ = 2L = 4 m. Thus, f = 343 m/s / 4 m = 85.75 Hz, approximately 85 Hz.

The fundamental frequency is given by f = v/λ; for a pipe open at both ends, λ = 2L, so f = v/(2L) = 343/(2*2) = 42.875 Hz.

The equation x(t) = A e^(-bt) cos(ωt) describes the motion of a damped harmonic oscillator.

The equation of motion for a damped harmonic oscillator includes a damping term and is given by m d²x/dt² + b dx/dt + kx = 0.

The equation of motion for a damped oscillator includes a damping term (b dx/dt) along with the restoring force (kx).

Inside a uniform sphere, the gravitational field strength varies linearly with distance from the center, so at R/2 it is g/2.

g = GM/r², at 3R, g = GM/(3R)² = GM/9R².

Gravitational field strength (g') = g / (distance^2) = g / (3R)^2 = g / 9.

g = GM/r²; at 3R, g = GM/(3R)² = G/9.

g = GM/r²; at 4R, g = GM/(4R)² = GM/16R².

Gravitational field strength g = GM/r². At 4R, g = GM/(4R)² = GM/16R² = G/16.

The gravitational field strength g at the surface of a planet is given by g = GM/R^2.