Vibrations and differential equations.

benoconnell22
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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?
 
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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?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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