1. The image below shows simple harmonic motion of a box on a spring. If the spring constant is 100 Mm, find the following quantities: a. Period (1 mark) Amplitude (1 mark) Mass of the box (1 mark) Maximum speed (1 mark) 99.0 x (cm) . The equation U(x) = xe'\"" is the potential energy between a particle of mass m and the surface of some metal. The parameters a and )8 are known constants. a. Find the distance x0 which minimizes the potential energy as well as the minimum potential energy (binding energy) U0. (1 mark) b. Taylor Expand U(x) around thexo. truncating the series at n = 2. By comparing your result to the spring energy E5 = ikxz, find the 'spring constant' for this problem and find the period of oscillation from a small perturbation away from the minimum energy. (4 marks) 3. An object with a mass of 5 kg oscillates back and forth on a frictionless horizontal table on an ideal spring. When set in vertical motion, the object obeys the equation y(t) = (4.40 cm) cos[(3.43 rad/s) t]. a. Find the period of oscillation. (1 mark) h. Find the maximum acceleration. (1 mark) c. Find the spring constant. (1 mark) d. Find the maximum kinetic energy. (1 mark)