Question

A mass m = 550 g is hung from a spring with spring constant k = 2.8 N/m and set into oscillation at time t = 0. A second, identical mass and spring next to the first set is also set into motion. At what time t should the second system be set into motion so that the phase difference in oscillations between the two systems is pi/2?

Answer 1

Answer:

The second system must be set in motion $t=0.70s$ seconds later

Explanation:

The oscillation time, T, for a mass, m, attached to spring with Hooke's constant, k, is:

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

One oscillation takes T secondes, and that is equivalent to a 2π phase. Then, a difference phase of π/2=2π/4, is equivalent to a time t=T/4.

If the phase difference π/2 of the second system relative to the first oscillator. The second system must be set in motion $t=\frac{\pi}{2}\sqrt(\frac{m}{k})=\frac{\pi}{2}\sqrt(\frac{0.55}{2.8}= 0.70s)$ seconds later