Friday

April 18, 2014

April 18, 2014

Posted by **Michael** on Friday, November 19, 2010 at 10:02pm.

What is the time constant if the ball's amplitude has decreased to 2.90 cm after 31.0 oscillations?

- Physics -
**drwls**, Saturday, November 20, 2010 at 1:17am"Time constant" usually refers to nonoscillatory motion, with an exponential decay. Do you want the "damping constant" that relates the friction force to velocity? Or the constant term that describes the exponential decay of the amplitude of the oscillations?

The solution to the equation of motion is of the form

X = 8 exp(-t/T) cos wt

w = sqrt(k/m) = 5.34 rad/s

(Actually, the damping reduces the frequency of oscillation slightly)

Period = 2 pi/w = 1.18 s

31 oscillations require 36 seconds.

exp(-36/T) = 2.9/8.0 = 0.363

T = 35 seconds is an effective time constant for decay.

**Related Questions**

Physics - A spring with spring constant 20.0 hangs from the ceiling. A 590 ball ...

Physics - A spring with spring constant 20.0N/m hangs from the ceiling. A 590g ...

physics - a spring with a length of 22.0 centimeters hangs from a ceiling. when ...

physics - a 0.1 kg mass is suspended at rest from a spring near the Earth's ...

physics - If a 0.1 kg mass is suspended at rest from a spring near the Earth's ...

Physics - "Two springs are hooked together and one end is attached to a ceiling...

PHYSICS - a 0.1 kg mass is suspended at rest from a spring near the Earth's ...

Physics - A small ball is attached to one end of a spring that has an unstrained...

Physics - A small ball is attached to one end of a spring that has an unstrained...

Physics - A spring with a force constant of 5.4 N/m has a relaxed length of 2.63...