Answer:
Explanation:
Given:
Displacement, x = (2.5 m) cos[(6π rad/s)t + π/4 rad]
A.
At t = 7s,
x = 2.5 × cos(42π + π/4)
= 2.5 × cos(169/4 × π)
= 5/4 × sqrt2
= 1.77 m
B.
dx/dt = v = -(2.5 × 6π) × sin[(6π rad/s)t + π/4 rad]
= -15π × sin[(6π rad/s)t + π/4 rad]
At t = 7s,
= -15π × sin[(42π rad/s)t + π/4 rad]
= -15π × sin(169/4 × π)
= -15/2 × π × sqrt2
= -33.32 m/s
C.
dv/dt = a = -(2.5 × (6π)^2) × cos[(6π rad/s)t + π/4 rad]
= -90 × (π)^2) × cos[(6π rad/s)t + π/4 rad]
At t = 7s,
= -90 × (π)^2) × cos[(42π rad/s) + π/4 rad]
= -45 × (π)^2) × sqrt2
= -628.1 m/s^2
D.
Comparing ,
x = Acos(wt + phil)
With,
x = (2.5 m) cos[(6π rad/s)t + π/4 rad]
Phase angle, phil = π/4 rad
Since 2π rad = 360°
π/4 rad = 360/8
= 45°
E.
angular velocity, w = 2π/t
= 2π × f
Comparing the above equations,
w = 6π rad/s
Frequency, f = 6π/2π
= 3 Hz
F.
Period, t = 1/f
= 1/3
= 0.33 s.
