At the grocery store, you place some produce onto a scale that has a vertically hung spring supporting the produce. The spring has a spring constant of 16 N/m. Your produce bobs up and down with an amplitude of 20 cm, and the maximum speed it reaches is 0.4 m/s. How much does your produce weigh?

Question

At the grocery store, you place some produce onto a scale that has a vertically hung spring supporting the produce.  The spring has a spring constant of 16 N/m.  Your produce bobs up and down with an amplitude of 20 cm, and the maximum speed it reaches is 0.4 m/s.  How much does your produce weigh?

Elena · Answer

x=A•sinωt, v=dx/dt=A•ω•cosωt =v(max) •cosωt, v(max)= A•ω, ω = v(max)/A=0.4/0.2=2 rad/s. ω²=k/m, m= k/ω² =16/2²=4 kg, Weight = mg =4•9.8=39.2 N.