All Problems

Mechanical Oscillations

Problem 4.34

A body \(A\) of mass \(m_{1}=1.00 \mathrm{~kg}\) and a body \(B\) of mass \(m_{2}=\) \(=4.10 \mathrm{~kg}\) are interconnected by a spring as shown in Fig. \(4.9 .\) The body \(A\) performs free vertical harmonic oscillations with amplitude \(a=1.6 \mathrm{~cm}\) and frequency \(\omega=25 \mathrm{~s}^{-1}\). Neglecting the mass of the spring, find the maximum and minimum values of force that this system exerts on the bearing surface.

Reveal Answer
4.34.F=(m1+m2)g±±m1aω2=60 and 40 N.\begin{aligned} & 4.34 . & F=\left(m_{1}+m_{2}\right) g \pm \\ \pm & m_{1} a \omega^{2}=60 \text { and } 40 \mathrm{~N} . \end{aligned}