A 0.440-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 12.0 cm. (Assume the position of the object is at the origin at t = 0.) (a) Calculate the maximum value of its speed. cm/s (b) Calculate the maximum value of its acceleration. cm/s2 (c) Calculate the value of its speed when the object is 8.00 cm from the equilibrium position. cm/s (d) Calculate the value of its acceleration when the object is 8.00 cm from the equilibrium position. cm/s2 (e) Calculate the time interval required for the object to move from x = 0 to x = 4.00 cm. s

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants