a mass of .30kg is attached to a spring and set into oscillation on a horizontal

Question

a mass of .30kg is attached to a spring and set into oscillation on a horizontal frictionless surface. the simple harmonic motion of the mass is described by x(t)=(.28m)cos[(14 rad/s)t]. determine the following.

a) amplitude of oscillation for the oscillation mass in m

b) force constant for the spring in N/m

c) position of the mass after it has been oscillating for one half a period in m

d)position of the mass one-third of a period after it has been released in m

e) time it takes the mass to get to the position x= -.10m after it has been released in seconds

Explanation / Answer

a) A = 0.28 m

b) k =m*W^2 = 0.3*14^2 = 58.8 N/m

c) t = T/2 = pi/W = 3.14/14 = 0.224

x(t) = 0.28*cos(14*0.224) = ?0.2799 m

d) t = T/3 = 2pi/3W = 2*3.14/3*14 = 0.224 *(2/3) = 0.1493 s

x(t) = 0.28*cos(14*0.1493) = ?0.138 m

e) -0.1 = 0.28*cos(14t)

t = 0.086 s

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