Answer to Question #316923 in Mechanics | Relativity for bless

Question #316923

We have a horizontal spring with a mass attached oscillating with a maximum displacement of



A



on either side. At which intermediate displacement(s) the kinetic energy would equal the potential



energy [10]?



1
Expert's answer
2022-03-24T11:00:43-0400

Explanations & Calculations


  • The point is, the total energy the system has which is the maximum potential energy is equal to the sum of both potential and kinetic energies at a given instance.
  • Say the elastic constant is k\small k , then

Emax=12kA2P.E+K.E=EmP.E+P.E=Em(asP.E=K.E)2(12kx2)=12kA2x=A2\qquad\qquad \begin{aligned} \small E_{max}&=\small \frac{1}{2}kA^2\\ \\ \small P.E+K.E&=\small E_m\\ \small P.E+P.E&=\small E_m\cdots\cdots(as\,P.E=K.E)\\ \small 2\Big(\frac{1}{2}kx^2\Big)&=\small \frac{1}{2}kA^2\\ \small x&=\small \frac{A}{\sqrt2} \end{aligned}


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