This question is an exact duplicate of:
A weight of 0.12 Newtons stretches a spring by 3 cm. The 0.12 N weight is removed and a 1 Kg mass is attached to the spring. An external force F(t) is provided by a (external) rotating motor and is given by
F(t)=0.04cos(ωt) in Newtons
where the external frequency w can be adjusted. After it reaches the equilibrium position, the spring cannot sustain further elongations larger than 6 cm. The mass is set into motion by the external force F (so at time t=0 the mass is set at rest in the equilibrium position).
Find the spring constant k. Find the internal frequency of the system. Find the motion x(t) of the mass if ω=1.5 and decude the maximum elongation. Find the range of all safe frequencies ω.
Is this the correct ODE for the motion 1/32 x^''+4x=0.04 cos(ωt),where x(0)=0,x^' (0)=1/32