A particle executes linear SHM with frequency 0.20 Hz about the point x = 0. At

Question

A particle executes linear SHM with frequency 0.20 Hz about the point x = 0. At t = 0, it has displacement x = 0.31 cm and zero velocity. Determine the following values for the motion. Use t for the time as appropriate.

(a) the period?

(b) the angular frequency?

(c) the amplitude?

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

(e) the velocity at time t, using t for the time in seconds but not including any units?

(f) the maximum speed?

(g) the magnitude of the maximum acceleration?

(h) the displacement at t = 3.0 s?

(i) the speed at t = 3.0 s?

Explanation / Answer

a)
T=1/f
T=1/.2
T=5
b)
w=2f

w=.4

c)

A=.31cm

d)

x(t)=.31cos(.4t)

e)

v(t)=-.124sin(.4t)

f)

v=.124 cm/s

g)

a(t)=-.04962cos(.4t)

a=.04962 m/s2

h)

x(3)=-.25

i)

v(3)=.229 cm/s

Hope that helps

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