posted by julie .
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.
(b) Determine the speed of the mass when the spring is compressed 1.5 cm.
(c) Determine the speed of the mass when the spring is stretched 1.5 cm.
(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)
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