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

Question

An air-track glider attached to a spring oscillates with a period of 1.50s . At t=0s the glider is 5.40cm left of the equilibrium position and moving to the right at 39.2cm/s .

Part A
What is the phase constant?
?o =
Part B
What is the phase at t=0.5s?
?=

Part C
What is the phase at t=1.0s?
? =
Express your answer to three significant figures and include the appropriate units.


Part D
What is the phase at t=1.5s?
? =
Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

x(t)=Acos(wt+o) x(0)=Acos(o)=-5.40cm
v(t)=-Awsin(wt+o) v(0)=-Awsin(o)=39.2cm/s

A=amplitude w=angular frequency o=phase constant T=period

sin(o)/cos(o) = tan(o) = -v(0)/wx(0)

w= 2(pi)/T = 4(pi)/3

a) o=arctan(-39.2/(4pi/3)(-5.4) = 1.0476rad or pi/3
however, since the glider is moving to the right it is not in that quadrant, since tan repeats every pi
subtracting pi will give you the correct answer of -2(pi)/3

o= -2pi/3rad

O phase at variable time(in this case 0.5) o= phase constant w=angular frequency t=time
b)O=wt+o
O=(4pi/3)(0.5) - (2pi/3)
O=0rad

this works for any other time as well just change the 0.5s to the new time the other two variables won't change.

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