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A 2.00-kg object attached to a spring moves without friction (b=0) and is driven by an...

A 2.00-kg object attached to a spring moves without friction (b=0) and is driven by an external force given by the expression F = 3.00 sin (2 π t) , where F is in newtons and t is in seconds. The force constant of the spring is 20.0 N/m. Find (a) the resonance angular frequency of the system, (b) the angular frequency of the driven system, and (c) the amplitude of the motion. Please explain the solution.

The book gives the following answers, but I was only able to get b:

a) 3.16 s-1

b) 6.28 s-1

c) 5.09 cm

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Answer #1

1316 20 a) Wo

(b) From F = 3 sin(2π), the anqular frequenc y of the force is

omega =2pi=6.28: s^{-1}

(c The amplitude Aof a driven oscillator with b-0 qives

  Fo/m w_uỷ 3/2 (6.292-(3.167 -0.0509 772 5.09 cm

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