Uncertainty in weight = g * (uncertainty in mass) = 9.8 * 0.1 = ±0.98 N, rounded to ±1 N.

The time period T of a mass-spring system in simple harmonic motion is given by T = 2π√(m/k).

The restoring force in simple harmonic motion is given by Hooke's law, which states that the force is proportional to the displacement and acts in the opposite direction. Therefore, the restoring force is -kx.

The angular frequency ω is given by ω = √(k/m).

Tension T = mv²/r. If r is halved, T doubles for constant speed.

At the highest point, the centripetal force is provided by the weight. Minimum speed = √(g*r).

At the highest point, T + mg = mv²/r, thus T = mg - mv²/r.

At the highest point, the centripetal force is provided by the weight of the mass, so T + mg = mv²/r. For T = 0, mg = mv²/r.

At the bottom, T + mg = mv²/r; T = mv²/r - mg.

At the highest point, the centripetal force must equal the weight: mv²/L = mg, thus v = √(gL).

The work done against gravity when lifting a mass m to a height h is given by W = mgh.

The angular frequency ω is given by ω = 2πf. For f = 2 Hz, ω = 2π(2) = 4π rad/s.

Maximum velocity (v_max) = Aω = A(2πf) = 0.1 * (2π * 2) = 0.4 m/s.

Maximum velocity (v_max) = Aω, where ω = 2πf. Assuming f = 1 Hz, v_max = 0.1 * 2π * 1 = 0.2 m/s.

In a damped system, the damped frequency is always less than the natural frequency.

The angular frequency ω is related to the frequency f by the formula ω = 2πf. Therefore, ω = 2π × 2 = 4π rad/s.

The time period T is the reciprocal of frequency f. T = 1/f = 1/2 Hz = 0.5 s.

Angular frequency (ω) is given by ω = 2πf. Thus, ω = 2π * 3 ≈ 6 rad/s.

Angular frequency (ω) is given by ω = 2πf. Thus, ω = 2π(3) = 6 rad/s.

Period (T) is the reciprocal of frequency (f). T = 1/f = 1/3 = 0.33 s.

Period T = 1/f = 1/5 = 0.2 s.

New frequency (ω_d) = ω_n√(1-ζ²) = 3√(1-0.1²) ≈ 2.9 Hz.

Frequency (f) is the reciprocal of the period (T). f = 1/T = 1/2 = 0.5 Hz.

Frequency f is the reciprocal of the period T. Thus, f = 1/T = 1/4 = 0.25 Hz.

The fractional change in volume is given by ΔV/V = ΔP/B. Here, ΔP = 50 MPa = 0.05 GPa, so ΔV/V = 0.05/200 = 0.00025.

The fractional change in volume ΔV/V is given by ΔV/V = ΔP/B, where ΔP = 10 MPa and B = 200 GPa, resulting in 0.00005.

The change in volume ΔV/V = P/B, so ΔV/V = 50 MPa / 200 GPa = 0.025%.

Poisson's ratio is defined as the negative ratio of lateral strain to longitudinal strain, so a Poisson's ratio of 0.3 means the ratio is 0.3.

A material is considered elastic if it returns to its original shape after the removal of the applied stress.

Young's modulus (Y) = Stress / Strain = 100 MPa / 0.002 = 50 GPa.