A 2.00-kg object isattached to a spring and placed on a horizontal, smoothsurfac

Question

A 2.00-kg object isattached to a spring and placed on a horizontal, smoothsurface.

A horizontal force of20.0 N is required to hold the object at rest when it is pulled0.200 m

from its equilibriumposition (the origin of the x axis).The object is now released from rest

with an initialposition of xi =0.200 m, and it subsequently undergoes simple harmonic

oscillations. Find(a) the force constant of the spring, (b) the frequency of theoscillations,

and (c) the maximumspeed of the object. Where does this maximum speed occur?(d)

Find the maximumacceleration of the object. Where does it occur? (e) Find thetotal

energy of theoscillating system. Find (f) the speed and (g) the acceleration ofthe object

when its position is equal to onethird of the maximum value.

Explanation / Answer

  we are given with    m = 2.00 kg    F = 20.0 N    x = 0.200 m    xi = 0.200 m (a)    we know that    F = k x    so the force constant of the spring willbe    k = F / x       = 20.0 N / 0.200 m       = ........ N . m (b)     we know that     = (k / m)        = ....... rad / s    as = 2 f    the frequency will be    f = / 2      = ........ Hz (c)    the maximum speed of the object willbe    vmax = A            =....... m / s (d)    amax = 2A                 =........ m / s2 (e)    the total energy of the oscillating systemwill be    E = (1 / 2) k A2       = ......... J (f)    the speed will be    v = (A2 -x2)       = ........ m / s (g)    a = 2 x       = ........ m /s2

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