Answer to Question #271608 in Physics for jay

Question

Estimate the stiffness (k) of a spring in a child’s pogo stick if the child has a mass of 35 kg and bounces once every 2.0 seconds. [ANS = 350 N m^-1]

Answer 1

Given:

$m=35\:\rm kg$

$T=2.0\:\rm s$

The period of oscillation of a spring pendulum

$$T=2\pi \sqrt{\frac{m}{k}}$$

Hence, the stiffness of a spring

$$k=\frac{4\pi^2m}{T^2}=\frac{4*3.14^2*35}{2.0^2}=345.4\:\rm N/m\approx 350 \:N/m$$