# Harmonic motion, 2 masses

1. Apr 1, 2005

### kodee vu

Urgent! Damped Simple Harmonic Oscillation

The thread topic says 2 masses, but there is actually only one!
I'm not asking for the complete solution for this problem; I simply just don't know WHERE to start.... The question is as follows:

In Figure 15-15, a damped simple harmonic oscillator has mass m = 290 g, k = 70 N/m, and b = 75 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)?

The figure shows a "Rigid support" at the top, to which a spring is hooked. At the bottom of this spring is a rectangular mass. At the bottom of this mass extends a vane which falls into water as the spring elongates.

variables listed: k, m, b (damping constant)

Last edited: Apr 1, 2005
2. Apr 2, 2005

### Andrew Mason

The solution to the differential equation of motion:

$$m\ddot x + b\dot x + kx = 0$$ is

$$x = A_0e^{-\gamma t}sin(\omega t + \phi)$$

where $\omega^2 = \omega_0^2 - \gamma^2 = k/m - b^2/4m^2$

What is the time, t, after 20 cycles? (ie. $\omega t = 40\pi[/tex]?) What is [itex]\gamma t = bt/2m$?

What is the amplitude (maximum x) at this time?

AM

Last edited: Apr 2, 2005