Vibrations and differential equations.

[benoconnell22]

Homework Statement

Suppose the motion of a spring has natural frequency 1/2 and is undamped. If the weight attached is 32lb, write a differential equation describing the motion.

Homework Equations

my''+ky=F_ocosωt

32y"+8y=?

ω_o= (k/m)^.5

The Attempt at a Solution

→ .5=(k/32)^.5 → k=8

gamma=0

32y"+8y=?My problem is that I don't know how to find F_o or ω. Is this question referring to that of a no external force case? Or am I missing some equation that will help me find this?

 

[rock.freak667]

The question is implying that there is no external forcing to F₀ = 0. As for ω, they gave you the natural frequency f. How does this relate to the angular frequency ω?