A 1.10-kg object is attached to a spring and placed on frictionless, horizontal

Question

A 1.10-kg object is attached to a spring and placed on frictionless, horizontal surface. A horizontal force of 30.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations.

(a) Find the force constant of the spring.
N/m

(b) Find the frequency of the oscillations.
Hz

(c) Find the maximum speed of the object.
m/s

(d) Where does this maximum speed occur?
x =

Explanation / Answer

(a) The force constant is F/?x = 30/0.200; k = 150 N/m

(b) f = (1/2?)?[k/m] = (1/2?)?[150/1.1] = 1.85 Hz

(c) The displacement is given by A*sin(2?ft) A = initial deflection = 0.200. The velocity is the derivative of this or 2?fA*cos(2?ft). At max (where cos = 1) the velocity is 2?fA m/s

(d) The acceleration is the derivative of the velocity or -(2?f)

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