Solve this in English showing all steps used

Here's the solution to the spring problem: a) the spring constant. Step 1: Identify the forces acting on the mass at equilibrium. When the mass hangs in equilibrium, the upward force exerted by the spring (spring force, F_s) balances the downward gravitational force (F_g) acting on the mass. F_s = F_g Step 2: Express the forces in terms of known quantities. The spring force is given by Hooke's Law: F_s = kx, where k is the spring constant and x is the extension. The gravitational force is: F_g = mg, where m is the mass and g is the acceleration due to gravity. Given: m = 0,5 kg x = 10 cm = 0,1 m (converting cm to m) g = 10 m/s^2 Step 3: Equate the forces and solve for the spring constant (k). kx = mg k(0,1 m) = (0,5 kg)(10 m/s^2) k(0,1 m) = 5 N k = 5 N0,1 m k = 50 N/m The spring constant is 50 N/m. b) the period of oscillation. Step 4: Use the formula for the period of oscillation of a mass-spring system. The period of oscillation (T) for a mass m attached to a spring with constant k is given by: T = 2 sqrt((m)/(k)) Step 5: Substitute the known values and calculate the period. m = 0,5 kg k = 50 N/m (from part a) T = 2 sqrt(0,5 kg)50 N/m T = 2 sqrt(0,01 s)^2 T = 2 (0,1 s) T = 0,2 s Using ≈ 3,14159: T ≈ 0,2 × 3,14159 s T ≈ 0,628 s The period of oscillation is 0,628 s. Send me the next one 📸