(b) A horizontal spring with force constant 1000N/m is attached at one end with a mids of 20 kg which is kept on a horizontal frictionless table The other end of the string is attached to a fixed support. If the mass is pulled 10 cm from its equilibrium position along the table and released, calculate the following for the mass when it is 5 cm from the equilibrium position:I (i) the velocity (ii) the acceleration . (iii) the potential crergy (iv) the kinetic energy

To solve this problem, we will use the principles of simple harmonic motion (SHM) and energy conservation. The mass-spring system follows Hooke's Law, and the total mechanical energy is conserved.Given:- Spring constant - Mass - Initial displacement - Displacement at the point of interest **(i) Velocity:**The total mechanical energy in the system is conserved and is given by: At any position , the total energy is the sum of kinetic energy (KE) and potential energy (PE): Setting these equal gives: Solving for : Substitute the values: **(ii) Acceleration:**Acceleration in SHM is given by: Substitute the values: **(iii) Potential Energy:**Potential energy at displacement is: Substitute the values: **(iv) Kinetic Energy:**Kinetic energy can be found using the total energy or directly from the velocity: Using the energy conservation approach: Thus, the answers are:- Velocity: - Acceleration: - Potential Energy: - Kinetic Energy: