A guitar string is pulled at a point P a distance of 3 cm above its resting position. It is then released and vibrates in damped harmonic motion

damped-harmonic

#1

A guitar string is pulled at a point P a distance of 3 cm above its resting position. It is then released and vibrates in damped harmonic motion with a frequency of 165 cycle sper second. After 2 seconds it is observed that the amplitude of the vibration at point P is .6 cm. Find the damping constant c. Then Find an equation that describe the position of the point P above its rest position as a function of time. Take t=0 to be the instant the string is released.

Answer:

a)3e^-2c=0.6,
e^-2c=0.6/3,
e^-2c=0.2,
e^2c=5,
ln5=2c,
c=ln5/2

b)w=2pif,
w=2.pi.165,
w=330pi
f(t)=3e^-0.87 cos(330.pi.t)