(Solved): Physics Assignment 1 Question 1 Consider the ideal spring, aligned on the z axis, with the equilibri ...

Physics Assignment 1 Question 1 Consider the ideal spring, aligned on the z axis, with the equilibrium point at z = 0. Hooke’s law in this case is Fs = ?kz. The angular frequency is still ? = ? k m in this case. 1. Using Newton’s second law, determine the equation of motion for the ideal spring aligned on the z axis. 2. The solution to the equation of motion (part 1.) is z(t) = B cos (?t + P ), where B is the amplitude and P is the phase constant. Show that this is indeed a solution to the equation of motion you found in 1. by direct substitution of this solution into the equation of motion. 3. Starting from the solution in part 2., and using the initial con- ditions z(0) = z0 and vz (0) = vz0, determine expressions for the amplitude B and phase constant P that depend only on the initial conditions and angular frequency ?. 4. Starting from the total mechanical energy E of the ideal spring, and the solution z(t) = B cos (?t + P ), show that the total energy of the ideal spring along the z axis is E = 1 2 kB2. 5. If the spring constant is k = 50N/m and the mass on the spring is 2kg, what is the i) angular frequency ?, ii) frequency f and iii) period T of oscillations?