A weight is oscillating on the end of a spring. The position of the weight relative to the point of equilibrium is given by y=1/12(cos8t-3sin8t), where y is the displacement (in meters) and t is the time (in seconds). Find the times when the weight is at the point of equilibrium (y=0) for 0

Question

A weight is oscillating on the end of a spring. The position of the weight relative to the point of equilibrium is given by y=1/12(cos8t-3sin8t), where y is the displacement (in meters) and t is the time (in seconds). Find the times when the weight is at the point of equilibrium (y=0) for 0<=t<=1.

Reiny · Answer

1/12(cos8t-3sin8t) = 0 cos8t-3sin8t = 0 3sin8t = cos8t sin8t/cos8t = 1/3 tan 8t = 1/3 8t = .32175 or 8t = π+.32175 t = .0402 or t = .4329

Damon · Answer

cos 8t = 3 sin 8 t

tan 8t = sin 8t/cos 8t = .333333333333333
8 t = 18.4 degrees
t = 2.3 in degrees
t = 2.3 *pi/180 = .04014 seconds if you do trig in radians
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check t = .04014
8 t = .321 radians or 18.4 deg
cos 18.4 = .949
3 sin 18.4 = .947 pretty close