An air-track glider attached to a spring oscillates with a period of 1.50 s . At t=0s the glider is 5.30 cm left of the equilibrium position and moving to the right at 38.5 cm/s .
A.) What is the phase constant?
B.) What is the phase constant at t=1.5s?
A.) Since Equation of oscillation is given by,
x(t) = A*sin(w*t + ) eq(1)
here, x(t) = Position
A = Amplitude
t = time
w = 2*pi/T
T = time period
= phase constant
at, t = 0
x(0) = -5.30
w = 2*pi/1.50 = 4*pi/3
So, -5.30 = A*sin(w*0 + )
-5.30 = A*sin
now differentiate eq(1) with respect to 't',
dx(t)dt = v(t) = A*w*cos(w*t + )
at, t = 0
v(0) = +38.5 = A*w*cos(w*0 + )
38.5 = A*(4*pi/3)*cos
By dividing bold equations,
-5.30/38.5 = [1/(4*pi/3)]*tan
tan = (4*pi/3)*(-5.30/38.5)
= arctan[(4*pi/3)*(-5.30/38.5)]
= -29.97 deg
= -pi/6 rad
B.)
Phase constant at time 't' is given by,
(t) = w*t +
given, t = 1.5 s
So, (t) = (4*pi/3)*1.5 + (-pi/6) = 2*pi - pi/6
(t) = 11*pi/6
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