A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g = 10 m/s ^2 )

Step-by-step solution

At equilibrium, the restoring force of the spring balances the weight of the mass: mg = kx₀ k = mg x₀ = 0.2 10 2 10⁻³ = 1000 N/m The frequency of oscillation is given by: f = 1 2 k m f = 1 2 1000 0.2 = 1 2 5000 = 10 50 2 = 5 50 Hz The maximum energy in the spring corresponds to its maximum elastic potential energy, which occurs at the maximum extension. Maximum extension x_ max = x₀ + A = 2 mm + 2 mm = 4 mm = 4 10⁻³ m Maximum energy in the spring U_ max = 1 2 k x_ max ^2 U_ max = 1 2 1000 (4 10⁻³)^2 U_ max = 500 16