physics
posted by julie on .
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 onehalf the maximum speed?
a,b,c are right. im just having trouble with (d)

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