Consider an ideal spring with a point mass m on its end, 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 = q k m in this case.

i). Find the equation of motion for the mass at the end of the ideal spring described above using Newton's Second Law.

ii). The solution to the equation of motion for part i) is: z(t) = B cos (t + P ) (3.1) ... where B is the amplitude and P is the phase constant. Prove that this is a solution to the equation of motion you found in i) by substituting this solution into the equation of motion.

iii). Find the functions for the velocity vz (t) and acceleration az (t) of the mass attached to the spring.

iv). Calculate the velocity and acceleration of the mass on the spring at time t = 20 s, if: the amplitude B = 2 m; phase con- stant P = 0; spring constant k = 50 N/m; and mass m = 3 kg. v). In this question, we approximated the mass attached to the ideal spring

Question 3 Consider an ideal spring with a point mass m on its end, aligned on the z-axis, with the equilibrium point at z = 0. Hooke's law in this case is F, = kz. The angular frequency is w = yz in this case. i). ii). Find the equation of motion for the mass at the end of the ideal spring described above using Newton's Second Law. The solution to the equation of motion for part i) is: z(t) = Bcos(wt + P) (3.1) .. where B is the amplitude and P is the phase constant. Prove that this is a solution to the equation of motion you found in i) by substituting this solution into the equation of motion. Find the functions for the velocity v,(t) and acceleration a,(t) of the mass attached to the spring. . Calculate the velocity and acceleration of the mass on the spring at time = 20 s, if: the amplitude B = 2 m; phase con- stant P = 0; spring constant k = 50 N/m; and mass m = 3 kg. . In this question, we approximated the mass attached to the ideal spring as a point mass. Explain why we do this in physics. Is it an accurate way to describe the motion of an object