A particle executes linear SHM with frequency 0.23 Hz about the point x = 0. At

Question

A particle executes linear SHM with frequency 0.23 Hz about the point x = 0. At t = 0, it has displacement x = 0.47 cm and zero velocity. Determine the following values for the motion. Use t for the time as appropriate.

(a) the period
s
(b) the angular frequency
rad/s
(c) the amplitude
cm

(d) the displacement x(t), using t for the time in seconds but not including any units
x(t) = cm

(e) the velocity at time t, using t for the time in seconds but not including any units
v(t) = cm/s


(f) the maximum speed
cm/s
(g) the magnitude of the maximum acceleration
cm/s2
(h) the displacement at t = 3.0 s
cm
(i) the speed at t = 3.0 s
cm/s

Explanation / Answer

a)period =1/f = 1/.23 = 4.35 s b)w= 2 pi .23 =1.445rad/s c)xo =.47 cm d)x= .47 cos(wt) e) v= (xo)w sinwt = .47x1.445 sinwt = .679sinwt f)max speed = (xo)w= .679cm/s g) max acceleration = (xo) w^2 = .98 cm/s^2 h) at t=3s x= .47cos(1.445x3)= .173cm i) at t=3s v= .679sin(1.445x3) = .63cm/s

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