Answer:(a) displacement= 6.0m
(b) velocity = 8.996m/s
(c) acceleration
(d) phase of motion= 2.999
(e) frequency= 1.499hz
(f) period of motion= 0.667sec
Explanation:Given that,
X= (6.0m) cos (3πrad/s)t + π/3rad...(i)
Compare equation (i) to wave equation,
Y= A cos (wt) + kx...(ii)
(a) displacement which is also known as amplitude A. So by comparing equation (i) & (ii), we have A= 6.0m
Therefore,displacement= 6.0m
(b) velocity=B/T (where B= wavelength and T=period)
Wavelength B=2π/k (where k=π/3,comparing the two equations)
Therefore, wavelength B=2π÷π/3=6
Period T= 2π/w (where w=3π,comparing the two equations)
Therefore, period T=2π÷3π=0.667sec
Therefore, Velocity V=B/T=6/0.667=8.996m/s
(d)phase of motion=t/T (where t= elapsed time and T=period)
T=0.667sec ( from (c) solving for velocity)
t=2.0s, as given in the question
Therefore, phase of motion= t/T=2/0.667=2.999
(e) frequency=1/T (where T is the period)
T=0.667secs (recall from (c) while solving for velocity)
Therefore, frequency=1/T=1/0.667=1.499hz
(f) period=1/f (where f= frequency)
Therefore, period=1/f=1/1.499=0.667secs.
