An air-track glider attached to a spring oscillates with a period of 1.50 s. At

Question

An air-track glider attached to a spring oscillates with a period of 1.50 s. At t = 0 s the glider is 4.90 cm left of the equilibrium position and moving to the right at 35.6 cm/s What is the phase constant? Express your answer to three significant figures and include the appropriate An air-track glider attached to a spring oscillates with a period of 1.50 s. At t = 0 s the glider is 4.90 cm left of the equilibrium position and moving to the right at 35.6 cm/s What is the phase constant? Express your answer to three significant figures and include the appropriate units. phi = -2.09 rad Answer Requested What is the phase at t = 0.5 s? Express your answer as an integer and include the appropriate units. Phi = _______Value _______Units

Explanation / Answer

x = A sin(w t + phi )

w = 2pi / T = 2pi / 1.50 = 4pi/3 rad/s

at t = 0

x = Asin(phi)

- 4.90 = A sin(phi) ...... (i)

and v = dx/dt = A w cos(phi)

35.6 = A w cos(phi) ...... (ii)

(i) / (ii) =>

tan(phi)/ w = - 4.90 / 35.6

tan(phi) = - 0.5765

{ sin is -ve but cos is +ve )

phi = - 0.52 rad

Ans(A) : - 0.50 rad

(B) at t = 0.5 s

phase = wt + phi

= (4pi/3 x 0.5) - 0.5

= 1.59 rad

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