A solid metal block with a mass of 1.40 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The block is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 22.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The block oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? 110 N/m (b) What is the frequency of the oscillations (in Hz)? 2.28 How is angular frequency related to the spring constant and mass? How is frequency related to angular frequency? Hz (c) What is the maximum speed of the block (in m/s)? 2.87 How is maximum speed related to angular frequency and amplitude? Note you can calculate the maximum speed by conservation of energy or by the taking the derivative of a sinusoidal position function if you do not remember the relationship. m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? x = 0.200 What is the speed at the maximum displacement points? At what point does the force change direction, so that in the next instant the object begins to slow down? m (e) What is the maximum acceleration of the block? (Enter the magnitude in m/s.) 32.8 How is the maximum acceleration related to angular speed and amplitude? m/s (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? x = 0.200 m (g) What is the total mechanical energy of the oscillating spring-block system (in J)? 2.2 (h) What is the speed of the block (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? 0.787 What is the position x in terms of amplitude? Using conservation of energy, how is kinetic energy and elastic potential energy related to the total mechanical energy? Can you use this to solve for speed? m/s (i) What is the magnitude of the acceleration of the block (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? -2.11 What is the spring force at this position? How is the spring force related to the acceleration? m/s