Please answer 10. -6 points My Notes I GioCP2 11.P.066 A mass of 3.3 kg is relea

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10. -6 points My Notes I GioCP2 11.P.066 A mass of 3.3 kg is released down a frictionless slope from a height of h 8 m. When it reaches the bottom of the slope, it undergoes a completely inelastic collision with a mass of 1.0 kg attached to a spring of spring constant k 5.5 kN/m as illustrated in the figure below. The combined mass then undergoes periodic motion. Calculate the following. (a) maximum velocity of two mass system m/s (b) frequency HZ (c) maximum amplitude (d) period (e) Determine expressions for position as a function of time and velocity as a function of time for the combined mass of this oscillating system. (Use the following as necessary: t.) x(t) v(t)

Explanation / Answer

u1 = sqrt(2gh) = sqrt(2*9.8*1.8) = 5.9396 m/s

m1u1 + m2u2 = m1v1 + m2v2

3.3*5.9396 + 0 = 4.3*v2

v2 = 4.558m/s

a) max vel = 4.558 m/s

b) w/2pi = sqrt(k/m)/(2*3.142) = sqrt(5500/4.3)/(2*3.142) = 5.691 Hz

c) 0.5mv^2 = 0.5kA^2

A = sqrt(m/k)v = sqrt(4.3/5500)*4.558 = 0.12744m

d) T = 2*3.142*sqrt(4.3/5500) = 0.1757 s

e) x(t) = 0.12744sin(35.764t)

v(t) = 4.558cos(35.76t)

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