All Problems

Mechanical Oscillations

Problem 4.59

Two balls with masses m1=1.0 kgm_{1}=1.0 \mathrm{~kg} and m2=2.0 kgm_{2}=2.0 \mathrm{~kg} are slipped on a thin smooth horizontal rod (Fig. 4.19). The balls are interconnected by a light spring of stiffness x=24 N/m.x=24 \mathrm{~N} / \mathrm{m} . The lefthand ball is imparted the initial velocity v1=12 cm/s.v_{1}=12 \mathrm{~cm} / \mathrm{s} . Find: (a) the oscillation frequency of the system in the process of motion; (b) the energy and the amplitude of oscillations.

Reveal Answer
4.59. (a) ω=x/μ=6 s−1\omega=\sqrt{x / \mu}=6 \mathrm{~s}^{-1} (b) E=1/2μv12=5mlJ,a=v1/ω=E=1 / 2 \mu v_{1}^{2}=5 \mathrm{ml} J, a=v_{1} / \omega= =2 cm.=2 \mathrm{~cm} . Here μ=m1m2/(m1+m2)\mu=m_{1} m_{2} /\left(m_{1}+m_{2}\right)
Prev
Next