A 200 g block hangs from a spring with spring constant 16 N/m . At t=0s the bloc

Question

A 200 g block hangs from a spring with spring constant 16 N/m . At t=0s the block is 18 cmbelow the equilibrium point and moving upward with a speed of 89.0 cm/s . What are the block's
Part A
What is the block's oscillation frequency?
Express your answer using two significant figures.
Part B
What is the block's distance from equilibrium when the speed is 57 cm/s ?
Express your answer using two significant figures.
Part C
What is the block's position at t=3.0s?
Express your answer using two significant figures.

Explanation / Answer

Given mass of block m = 200 g = 0.2 kg, k = 16 N/m

at t = o s x = 18 cm,v0 = 89.0 m/s

we know
a)   the timeperiod T = 2pisqrt(m/k),
   f = 1/T = 1/2pi*sqrt(k/m)
           = (1/(2*3.14))(sqrt (16/0.2))
       = 1.42 Hz

and W = 2*pi*f = 2*3.14*1.42 = 8.91 rad/s

   x(t) = A Cos(wt) = 18 cm ==> A = 0.18m

   v(t)= - AW Sin (wt)

   v(t)= - AW Sin (wt)= 0.57 m/s
   => - 0.18*8.91*Sin (8.91t)= 0.57 m/s
              t = 2.29 s

b)   x(t) = ACos Wt = 0.18 *Cos(8.91*2.29) = 0.17 m

c)    x(3) = ACos wt
        = 0.18*Cos(8.91*3)
               = 0.16 m

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