please see the attached question A guitar string vibrates at a frequency of 440

Question

please see the attached question

A guitar string vibrates at a frequency of 440 Hz. A point at its center moves in SHM with an amplitude of 3.0 mm and a phase angle of zero. a. Write an equation for the position of the center of the string as a function of time. b. What are the maximum values of the magnitudes of the velocity and acceleration of the center of the string? c. The derivative of the acceleration with respect to time is a quantity called the jerk. Write an equation for the jerk of the center of the string as a function of time, and find the maximum value of the magnitude of the jerk.

Explanation / Answer

w = 2*pi*f = 2*3.14*440 = 2763.2

a ) Y = A*sinwt = 3mm*sinwt = (3.0mm)sin(2763.2t)

b) V max = A*W = 3*10^-3*2763.2 = 8.2896 m/s

amax = W^2*A = -22905.822 m/s^2

c) Jerk = da/dt = d(W^2*A*sinwt)/dt = W^3*A*coswt

jerk max = W^3*A = 63.293*10^6 m/s^3

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