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 (A² - x²)^1/2    x is displacement of mass from equilibrium positon.
V = 7.42 ( 4² - 1.5²)^1/2 = 27.5 cm/sec

c) Again V = 27.5 cm/sec, as x² is same for compression of spring or extension of spring by 1.5 cm.

d) Vm/2 = wA/2 = w (A² - x²)^1/2
A/2 = (A² - x²)^1/2
A²/4 = A² - x²
x² = 3A²/4
x = +/- root3 A/2