Asmall object is attached to the end of a relaxed, horizontal spring whose opposite end is fixed. the spring rests on a frictionless surface. let the initial position of the object be defined as x-0. the object is pulled to position x = a and then released, after which it undergoes simple harmonic motion. in one full cycle of its motion, the total distance traveled by the object is 2 4 o 4a

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h- (the hydride ion, which has one proton and two electrons) to an energy of 5 mev to 20 mev. this ion has a mass very close to that of a proton because the electron mass is negligible—about 1 2000 of the proton’s mass. a typical magnetic field in such cyclotrons is 1.9 t. (a) what is the speed of a 5.0-mev h-? (b) if the h- has energy 5.0 mev and b = 1.9 t, what is the radius of this ion’s circular orbit?