The displacement of a harp string

Question

The displacement, x, in millimeters, of a harp string, t, seconds after it is initially plucked is modeled by the function, x(t)=12sin(20πt)

 

a) what are the amplitude and period of this function?

 

b) how many vibrations will it complete in 1 second?

 

c) Find the displacement after 0.08 seconds.

 

 

Answer 1

a)

 

x_max = 12 mm

 

ω = 20π rad/s

 

T = 2π / ω = 2π / (20π rad/s) = 0.1 s

 

b)

 

f = ω / (2π) = (20π rad/s) / (2π) = 10 Hz

 

c)

 

x(0.08) = 12 sin [20π(0.08)] mm = -11.4 mm