The period T is given by T = 2π√(m/k). Here, T = 2π√(2/200) = 2π√(0.01) = 2π(0.1) = 0.2π ≈ 0.63 s.

Angular frequency (ω) = 2πf = 2π(3) = 6 rad/s.

The period of a mass-spring system is T = 2π√(m/k). Halving the mass does not change the period since it is independent of mass in this case.

Angular frequency ω = 2πf = 2π(3) = 6 rad/s.

Angular frequency (ω) = 2πf = 2π(3) = 6 rad/s.

Angular frequency ω = 2π/T = 2π/2 = π rad/s ≈ 3.14 rad/s.

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

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

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

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

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

Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.

The period of a simple pendulum is given by T = 2π√(L/g). If L is doubled, T becomes T' = 2π√(2L/g) = √2 * T ≈ 1.41 s.

The period of a pendulum is given by T = 2π√(L/g). If L is increased to 4L, T becomes 2π√(4L/g) = 2T = 2 seconds.

The period T = 2π√(L/g). If L is increased by a factor of 4, T increases by a factor of √4 = 2.

The period T = 2π√(L/g). If L is tripled, T becomes √3 times longer, so T = 2 s.

Length L = (gT^2)/(4π^2) = (9.8 * 1^2)/(4 * π^2) ≈ 1 m.

Angular frequency (ω) = 2π/T = 2π/1.5 = 4π/3 rad/s.

The period T of a simple pendulum is given by T = 2π√(L/g). For length 4L, T' = 2π√(4L/g) = 2T.

In simple harmonic motion, the restoring force is proportional to the displacement from the equilibrium position.

The time period (T) is the reciprocal of frequency (f). T = 1/f = 1/5 = 0.2 s.

ω = V_max/A = 2/0.1 = 20 rad/s.

Maximum potential energy (PE) = (1/2)kA^2 = (1/2)(200)(0.1^2) = 1 J.

T = 2π√(m/k) = 2π√(2/200) = 1 s.

The total energy E is proportional to the square of the amplitude. If the amplitude is halved, the new energy will be E/4.

Total energy E = (1/2)kA^2. 50 = (1/2)k(0.1^2) => k = 500 N/m.