(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A mass 'm' is attached to the free end of a spring (unstretched = l) of spring constant 'k' and suspended vertically from ceiling. The spring stretches by Δl under the load andd comes to equilibrium position. The mass is pushed up vertically by "A" from its equilibrium position and released from rest. The mass-spring executes vertical oscillations. Show from energy considerations that the total energy of the spring-mass system is (1/2)k[Δl^2 + A^2] assuming the gravitational potential energy is zero at the equilirium position of the mass 'm'

2. Relevant equations

PE= (1/2)kx^2

KE= (1/2)mv2

Total Energy = PE + KE

Oscillating systems = x=Asinωt

v= Aωcosωt

3. The attempt at a solution

Since energy is conserved, I should get (kx^2/2) + (mv^2/2) = E. Therefore, I can substitute in (kA^2sin^2ωt)/2 + (mA^2ω^2cos^2ωt)/2 = E

Since ω^2 = k/m, I get (kA^2/2)sin^2ωt + (kA^2/2)cos^2ωt = E.

By using trig identities, I can reduce this to E = (KA^2)/2.

This is close to what I'm supposed to get, but I'm not quite there yet. Can anyone help me?

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# Homework Help: Energy involving springs

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