Draw a plots of mechanical energy, potential energy and kinetic energy versus displacement for different position of a motion of a block attached to a spring.

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The equation of mechanical energy for a block attached to the end of spring at the point between maximum distance $x_{m}$ and zero is,

$\mathrm{E}=\frac{1}{2} k x_{m}^{2}$

Equation of potential energy is $\mathrm{V}(x)=\frac{1}{2} k x_{m}^{2}$ and equation of kinetic energy is $\mathrm{K}=\frac{1}{2} m v_{m}^{2}$ At equilibrium position $x=0$ the speed is maximum and hence the kinetic energy is maximum that means $\frac{1}{2} m v_{m}^{2}=\frac{1}{2} k x_{m}^{2}$

displacement

kinetic

energy[k]

potential

energy[v]

total

energy[e]

$x_{m}$ $0$ $\frac{1}{2} k x_{m}^{2}$ $\frac{1}{2} k x_{m}^{2}$
$0 $ $\frac{1}{2} m v_{m}^{2}$ $0$ $\frac{1}{2} k x_{m}^{2}$
$-x_{m}$ $0$ $\frac{1}{2} k x_{m}^{2}$ $\frac{1}{2} k x_{m}^{2}$

 

887-s95

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