Question: A 3kg block is attached to an ideal spring with a force constant k = 200N/m. The block given + + direction of magnitude u = 12 m/s. Find a. The amplitude b. The phase angle c. Write an equation for the position as a function of time?

1 Answer
Apr 30, 2018

Given,

#m = 3"kg"#

#k = (200"N")/"m"#

#nu_"max" = (12"m")/"s"#

Now recall,

#nu_"max" = A * sqrt(k/m)#

Hence,

#=> A = nu_"max"/(sqrt(k/m)) approx 1.5"m"#

Let's derive the period (e.g. phase angle),

#T = 2pi * sqrt(m/k) approx 0.77"s"#,

and construct an equation in the form:

#x = Asin((2pi*t)/T)#.

Graphing,

#x(t) = 1.5sin(8.16t)#

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