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16Nm− k = and m = 0.1 kg.The system is oscillating with an amplitude of 0.20 m. i) Calculate the angular frequency of oscillation. ii) Obtain an expression for the velocity of the block as a function of displacement and calculate its value at x = 1.0 m. iii) Also calculate energy of the spring-mass system.

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equation of motion and force: F = m a = m d²x/dt² = - k x d²x/dt² = - k/m x

let x = A Sin (ωt + Ф) then d²x/dt² = - A ω² Sin(ωt+Ф) = - ω² x

k = 116 N/m or 16 N/m ??? which one ? m = 0.1 kg A = 0.20 meters

SHM : angular frequency = ω = √(k/m) = √(116/0.1) = 34 rad/sec if k = 16 N/m, ω = √160 = 4√10 rad/sec ========== x = A Sin (ωt + Ф) = displacement from the mean position v = velocity of the particle executing the SHM v = dx/dt = A ω Cos (ω t + Ф) v = ω √A² - x² ) = ω A √[1 - x²/A² ] ==================== x = 1.0 m this value is not possible, as amplitude is 0.20 m. SO x has to be less than 0.2 m. Is it 0.1 meters ? x has to be less than or equal to amplitude.

Energy of the spring mass system : = 1/2 m v² at the mean equilibrium position , as x = 0 and PE = 0 = 1/2 k A² at the extreme position when x = A, as v = 0 and KE = 0. = 1/2 * 0.1 kg * 0.20² = 0.002 Joules