The position of a particle is given by the expression x = 4.00 cos (6.00πt + π), where x is in meters and t is in seconds.

(a) determine the frequency. hz (b) determine period of the motion. s
(c) determine the amplitude of the motion. m
(d) determine the phase constant. rad
(e) determine the position of the particle at t = 0.350 s.

(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.

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