An air-track glider attached to a spring oscillates with a period of 2.85 s. At

Question

An air-track glider attached to a spring oscillates with a period of 2.85 s. At t-0 s the glider is 1.36 cm left of the equilibrium position and moving to the right at 26.37 cm/s What is the phase constant? (in degrees) Submit Answer IncoretTries 67 revious Tries What is the phase at t-0 s? (in degrees) Tries O7 What is the phase at t=0.5 s? (in degrees) Tries O7 What is the phase at t=1 s? (in degrees) Submit Answer Submit Answer 209.8 Submit Answer Incorrect. Tries 17 Previous Tries What is the phase at t=1.5 s? (in degrees) Submit Answer Tries 0/7

Explanation / Answer

The general equation of the position

x(t) = A cos ( wt + phi)

at t= o

x(t) = A cos phi

differentiate with respect to time x(t) = A cos ( wt + phi_o)

v= - A w sin ( wt + phi)

at t= 0

v(0) = - A w sin phi

v(o)/ x(0) = -A w sin phi/ A cos phi

tan phi = - vo/ xo w

phi = tan^-1 ( - vo/ xo ( 2 pi/T)

= tan^-1 ( - 26.37/1.36 *( 2pi/2.85)) = 83.51 degree or 1.45 rad

subtract pi rad = 1.45 rad - 3.14 rad = -1.68 rad

(b)

phi(t) = wt + phi

= ( 2pi/T) t + phi

at t= 5 sec

= 2pi/2.85) ( 0.5) -1.68 rad

=-0.578 rad in degree -33.11 degree

at t= 1.0s

= 2pi/ 2.85 ( 1s) - 1.68 rad

=0.523 rad or 29.96 degree

at t= 1.5 s

= 2 pi/(2.85) ( 1.5) -1.68

=1.625 rad or 93.1 degree

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