Question

(9%) Problem 8: The midpoint M of a guitar string is pulled a distance d observed to undergo simple harmonic motion with a frequency f- 210 Hz. 1.7 mm from equilibrium and released. Point M is à 14% Part (a) Calculate the angular frequency o of oscillation in radians per second. Grade Summary Deductions 0% Potential 100% sin0 cos0 tan0 7 8 9 HOME Sabmissions Attempts remaining: 50 (0% per attempt) detailed view 4 cotan) asin) асos) 5 6 acotan tanh) Degrees sinh) atan) 1 2 3 cosh() cotanh) 0 + ND Radians vo LAR 1 give up Subenit Hint Hints: 0% deduction per hint. Hints remaining: 1 Feedback: 0% deduction per feedback 14 % Part (b) Assume the displacement of point M from equilibrium as a function of time t after release is of What is ma in meters? & 14% Part ( c) After the string is first released, how many seconds will elapse before it first reaches its equilibrium position? à14% Part (d) Calculate the maximum speed of point M during its oscillation vmax in meters per second. &14% Part ( e) Select the position(s) at which Point M reaches its maximum speed. There may be more than one point where Point M reaches maximum speed. à 14% Part (D Calculate the magnitude of the maximum acceleration experienced by point M during its oscillation aax in meters per square form x() mar cos(et + ) second. & 14% Part (g) Select the position(s) at which the acceleration of point M is maximized.

all questions

Answer 1

A)

Angular frequency, w = 2 pi x 210 = 1319.47 rad/sec

B)

X_max = 1.7 x 10^-3 m

C)

Time, t = 1/210 = 4.76 x 10^-3 sec

T = t/4 = 1.19 x 10^-3 sec

D)

V_max = 0.0017 x 1319.47 = 2.24 m/s

F)

Acceleration, a = 0.0017 x 1319.47^2 = 2959.7 m/s^2

G)

At x = - X_max

And x = X_max

Comment in case any doubt please rate my answer....