**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)