Answer:
(a) Frequency =
(b) Period = 3 Hz
(c) Amplitude = 4.0 cm
(d) phase constant =3.143
(e) position of the particle = 3.94 m.
Explanation:
x = 4.0 cos(6.00πt + π ) ................. equation 1
x = A cos (2πft - Φ )........................ equation 2
Where A = amplitude (m), f = frequency (hertz), Φ = phase constant.
Comparing the two equations above, equation above i.e equation 1 and equation 2
(a) 2πft = 6πt
Dividing both side by 2πt
∴f= 6πt/2πt = 3 Hz.
(b) f = 1/T
T = 1/f = 1/3 = 0.33 s
(c) Amplitude A = 4.0 cm
(d) phase constant (Φ) = 2πx/λ,
Comparing the two equations above,
Φ = π = 3.143
(e) substituting the value t= 0.350 s, into equation 1
x = 4.00 cos{6(3.143×0.350) + 3.143}
x = 4.00 cos(9.74)
x = 4 × 0.986
x = 3.94 m.
