Question

CHP 13

3) A horizontal object-spring system oscillates with an amplitude of 2.8 cm. If the spring constant is 280 N/m and object has a mass of 0.50 kg, determine each of the following values. (a) the mechanical energy of the system J (b) the maximum speed of the object m/s (c) the maximum acceleration of the object m/s2

Answer 1

(a) The easiest way to get the mechanical energy of this system is to calculate the potential energy of the mass/spring when the spring is compressed/stretched to 2.8 cm:
kx^2/2 = (280 N/m)(0.028 m)^2/2 = 0.10976 J

(b) vmax = A*ω, where ω^2 = k/m for a mass-spring system
vmax = (0.028 m)*sqrt(280 N/m / 0.50 kg)
vmax = 0.6626 m/s

(c) amax = A*ω^2
amax = (0.028 m)*(280 N/m / 0.50 kg)
amax = 15.68 m/s^2