The midpoint M of a guitar string is pulled a distance d = 1.2 mm from equilibrium and released. Point M is observed to undergo simple harmonic motion with a frequency f = 270 Hz.
Part (a) Calculate the angular frequency ω of oscillation in radians per second.
Part (b) Assume the displacement of point M from equilibrium as a function of time t after release is of the form x(t) = xmax cos(ωt +θ). What is xmax in meters?
Part (c) After the string is first released, how many seconds will elapse before it first reaches its equilibrium position?
Part (d) Calculate the maximum speed of point M during its oscillation vmax in m/s.
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.
Part (f) Calculate the magnitude of the maximum acceleration experienced by point M during its oscillation amax in m/s2.