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