Show that the conservation of energy holds also for the vertical spring where x is measured from the vertical equilibrium position (x_0 = mg/k) for a mass m.(adsbygoogle = window.adsbygoogle || []).push({});

This is what I did so far. Where do I go from here?

f = mg - kx_0 = 0

kx_0 = mg

E = KE + PE_grav + PE_spring

= ([mv^2]/2) - mg(x + x_0) + [(x + x_0)^2]/2

= ([mv^2]/2) - mgx - mgx_0 + (k/2)[x^2 + 2xx_0 + x_0^2]

= ([mv^2]/2) - mgx - mgx_0 + [(kx^2)/2] + xx_0k + [(kx_0^2)/(2)]

E_x0 = ([mv^2]/2) - mgx_0 + [(kx_0^2)/2]

Thanks for helping.

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# Homework Help: Vertical Oscillator

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