A particle moves so that position x in meters is given as a function of time t i

Question

A particle moves so that position x in meters is given as a function of time t in seconds by the equation x(t) = c1 cos(c2t + c3), where c1 = .0263 m, c2 = 356 s ^-1 , c3 = 1.43 .

Give numerical values for the following:
(a) Amplitude (m)
(b) Angular frequency (rad/s)
(c) Frequency (Hz)
(d) Period (s)
(e) Phase constant (rad)
(f) What is the position (m) of the particle at t = 3.00 ms?
(g) What is the velocity (m/s) of the particle at t = 3.00 ms?
(h) What is the acceleration (m/s2) of the particle at t = 3.00 ms?

Explanation / Answer

genereal equation is x(t) = A*cos(wt+phi)..

(a) Amplitude (m) = 0.0263m
(b) Angular frequency (rad/s) = C2 = 356 rad/sec
(c) Frequency (Hz) = f = w/(2*pi) = 356/6.284 = 56.65
(d) Period (s) = T = (1/f) = 0.0176 sec
(e) Phase constant (rad) = c3 = 1.43 rad
(f) What is the position (m) of the particle at t = 3.00 ms?

x(t) = 0.0263*cos(356*0.003+1.43) = -0.021m...

(g) What is the velocity (m/s) of the particle at t = 3.00 ms?

v(t) = dx/dt = -c1*w*sin(c2t+c3) = -0.0263*356*sin(356*0.003+1.43)= 5.62 m/sec...

(h) What is the acceleration (m/s2) of the particle at t = 3.00 ms?

a = dv/dt = c1*w^2*cos(c2t+c3) = 2661.456 m/sec^2

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