Saturday

February 28, 2015

February 28, 2015

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.

**Answer this Question**

**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 - One end of a massless coil spring is suspended from a rigid ceiling. ...

physics - One end of a massless coil spring is suspended from a rigid ceiling. ...

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 length of 22.0 centimeters hangs from a ceiling. when ...

Physics - In a room that is 2.69 m high, a spring (unstrained length = 0.28 m) ...

physics - In a room that is 2.78 m high, a spring (unstrained length = 0.30 m) ...

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