Question

A 0.33 kg object connected to a light spring with a force constant of 18.2 N/m oscillates on a frictionless horizontal surface. If the spring is compressed 4.0 cm and released from rest.

(a) Determine the maximum speed of the object.

______ cm/s

(b) Determine the speed of the object when the spring is compressed
1.5 cm.

__________cm/s

(c) Determine the speed of the object when the spring is stretched
1.5 cm.

________cm/s

(d) For what value of *x* does the speed equal one-half the
maximum speed?

________cm

Answer #1

Angular frequency of oscillations

w = (k/m)^{1/2} = 7.42 rad/sec

a) Maximam speed of object = wA (where a is amplitude of
oscillation = 4 cm)

Vm = 7.42*4 = 29.7 cm/sec

b) V = w (A^{2} - x^{2})^{1/2}
x is displacement of mass from equilibrium
positon.

V = 7.42 ( 4^{2} - 1.5^{2})^{1/2} = 27.5
cm/sec

c) Again V = 27.5 cm/sec, as x^{2} is same for
compression of spring or extension of spring by 1.5 cm.

d) Vm/2 = wA/2 = w (A^{2} -
x^{2})^{1/2}

A/2 = (A^{2} - x^{2})^{1/2}

A^{2}/4 = A^{2} - x^{2}

x^{2} = 3A^{2}/4

x = +/- root3 A/2

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