The figure below shows the displacement of a simple harmonic equilibrium in cent

Question

The figure below shows the displacement of a simple harmonic equilibrium in centimeters, where the displacement at t 10 ms is O. (4) Write an equation for the displacement of the oscillator as a function of time, with appropriate numerical values and units. a) b) What is the velocity of theoscillator at t= ) What is the next time after i 0 at which the displacement is 1 cm alS d) What is the second time 'after0 at which the displacement is +3 cm? 2 t? t? -0.03-0.02-0.01 0 0.01 0.02 0.03 0.04 0.05

Explanation / Answer

A = 5 cm

T = 2 x 10 ms = 20 ms

w = 2pi/T = 100 pi rad/s

(A) x = A sin(w t )

x = (5 cm) sin(100 pi t)

(B) v = dx/dt = (100pi x 0.05 m/s) cos(100pit)

at t = 0

v = 15.7 m/s

(C) - 1 = 5 sin(100 pi t)

t= 0.64 x 10^-3 s or 0.64 ms

(D) 3 = 5 sin(100 pi t)

t = 0.012 s or 12 ms

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