The position of a 0.30-kg object attached to a spring is described by x = (0.25 m) cos(0.2πt) (a) Find the amplitude of the motion.?
The position of a 0.30-kg object attached to a spring is described by
x = (0.25 m) cos(0.2πt)
(a) Find the amplitude of the motion.
m
(b) Find the spring constant.
N/m
(c) Find the position at t = 0.36 s.
m
(d) Find the object's speed at t = 0.36 s.
m/s
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Verified answer
For x(t) = 0.25m * cos(0.2πt),
v(t) = dx/dt = -0.25m * 0.2π * sin(0.2πt)
(a) A = 0.25 m
(b) k = mω² = 0.30kg * (0.2π rad/s)² = 0.12 kg/s² = 0.12 N/m
(c) x(0.36) = 0.25m * cos(0.2π*0.36) = 0.24 m
Make sure your calculator is in radians mode!
(d) v(0.36) = -0.25m * 0.2πrad/s * sin(0.2π*0.36) = -0.035 m/s
Hope this helps!