Homework Help: physics

Posted by julie on Tuesday, January 11, 2011 at 3:41pm.

A 0.44 kg object connected to a light spring with a spring constant of 22.0 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest.
(a) Determine the maximum speed of the mass.
28.28 cm/s
(b) Determine the speed of the mass when the spring is compressed 1.5 cm.
26.22 cm/s
(c) Determine the speed of the mass when the spring is stretched 1.5 cm.
26.22 cm/s
(d) For what value of x does the speed equal one-half the maximum speed?

a,b,c are right. im just having trouble with (d)

physics - drwls, Tuesday, January 11, 2011 at 3:48pm
When the speed is 1/2 of the maximum speed, the kinetic energy is 1/4 of the maximum value.

That means the potential energy is 3/4 of the total energy, which is also 3/4 of the maximum potential energy.

That in turn means that the deflection x is sqrt (3/4) or 0.866 of its maximum value, the 4 cm amplitude.

x = 3.464 cm

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