Q2 Jerk. A guitar string vibrates at a frequency of 410 Hz. A point at its cente
ID: 1272253 • Letter: Q
Question
Q2
Jerk. A guitar string vibrates at a frequency of 410 Hz. A point at its center moves in SHM with an amplitude of 4.0 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 t. (Keep the value of the amplitude in mm, Use any variable or symbol stated above along with the following as necessary: ). x(t) = (b) What are the maximum values of the magnitudes of the velocity and acceleration of the center of the string? velocity m/s acceleration m/s2 (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 (Keep the value of the amplitude in mm, Use any variable or symbol stated above along with the following as necessary: ). j(t) = Find the maximum value of the magnitude of the jerk. mm/s3
Explanation / Answer
x(t) = 0.004 sin(w t)
a. velocity = d/dt x(t) = w A cos( w t)
velocity = wA = 2*3.14*410*0.004 = 10.304 m/s
Accleration = w^2A = (2*3.14*410)^2(0.004) = 26545.288 m/s^2
Jerk = -w^3(Acoswt) = 6.83*10^7
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