# Problem: The device pictured in Figure 16.4 entertains infants while keeping them from wandering. The child bounces un a harness suspended from a door frame by a spring constant - K = 313.6 N/m.What is the child's maximum velocity if the amplitude of her bounce is 0.200 m? (Mass of the child is 8.0 kg).

###### FREE Expert Solution

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

The potential energy of a simple harmonic oscillator:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{K}}{{\mathbf{A}}}^{{\mathbf{2}}}}$

From the principal of conservation of energy, the maximum kinetic energy of a simple harmonic oscillator is equal to the maximum potential energy:

86% (254 ratings) ###### Problem Details The device pictured in Figure 16.4 entertains infants while keeping them from wandering. The child bounces un a harness suspended from a door frame by a spring constant - K = 313.6 N/m.

What is the child's maximum velocity if the amplitude of her bounce is 0.200 m? (Mass of the child is 8.0 kg).