Question

A 0.40-kg mass is attached to a spring with a force constant of k = 337 N/m, and the mass-spring system is set into oscillation with an amplitude of A = 3.1 cm. Determine the following. (a) mechanical energy of the system (b) maximum speed of the oscillating mass m/s (c) magnitude of the maximum acceleration of the oscillating mass m/s2

Answer 1

given
m = 0.40 kg
k = 337 N/m
A = 3.1 cm = 0.031 m

a) mechanical energy of the system, U = (1/2)*k*A^2

= (1/2)*337*0.031^2

= 0.162 J <<<<<<<<<-------------------Answer

b) angular fequency, w = sqrt(k/m)

= sqrt(337/0.4)

= 29.02 rad/s

v_max = A*w

= 0.031*29.02

= 0.900 m/s <<<<<<<<<-------------------Answer

c) a_max = A*w^2

= 0.031*29.02^2

= 26.1 m/s^2 <<<<<<<<<-------------------Answer