Question

A block or unkno n mass is attached to อ 27.0 cmfs spring with a spring constant of 5.00 N m and undergoes simple her onic motion wit en amplitude or 12.5 cm when the block is halfway between its equilibrium position and the end point, its speed is mees ed to be a) Calculate the mass of the black b) Calculate the periad of the motion. ) Calculate the maximum acceleration of the block. mis2

Answer 1

a) speed of block v = squareroot k/m (A^2 - x^2) (0.27)^2 = 5/m times [0.125^2 - (0.125/2)^2] m = 5/(0.27)^2 times 0.125^2 times 3/4 mass m = 0.804 kg b) w = squareroot k/m rightarrow 2 pi/T = squareroot k/m T = 2 pi times squareroot 0.804/5 = 2.52 sec Time period T = 2.52 sec c) maximum acceleration a_max = w^2 A = k/m A a_max = 5/0.804 times 0.125 = 0.7774 m/s^2