The displacement from equilibrium of an object in harmonic motion on the end of a spring is given below, where y is measured in feet and t is the time in seconds. Determine the velocity v(t) of the object when t = π/2.
y= 1/2 cos (3t) - 1/6 sin (3t)
v(pi/2) ft/sec=?
y= 1/2 cos (3t) - 1/6 sin (3t)
v(pi/2) ft/sec=?
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If y(t) = 1/2 cos(3t) - 1/6 sin(3t) is displacement, velocity is
dy/dt = 3*(1/2)*-sin(3t) - 3*(1/6)*cos(3t)
so v(t) = -3/2*sin(3t) - 1/2*cos(3t).
Let t = pi/2:
v(pi/2) = -3/2*sin(3*pi/2) - 1/2*cos(3*pi/2)
= -3/2*-1 - 1/2*0
= 3/2 = 1.5 feet/second.
dy/dt = 3*(1/2)*-sin(3t) - 3*(1/6)*cos(3t)
so v(t) = -3/2*sin(3t) - 1/2*cos(3t).
Let t = pi/2:
v(pi/2) = -3/2*sin(3*pi/2) - 1/2*cos(3*pi/2)
= -3/2*-1 - 1/2*0
= 3/2 = 1.5 feet/second.
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45.227 ft /s