A 30.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 6.00 cm on a frictionless, horizontal surface. (a) Find the total energy of the system. 72 mJ (b) Find the speed of the object when its position is 1.15 cm. (Let 0 cm be the position of equilibrium.) m/s (c) Find the kinetic energy when its position is 3.00 cm. mJ (d) Find the potential energy when its position is 3.00 cm. mJ

a) 72mJ

b) 0.33m/s

c) 54mJ

d) 18mJ

Explanation:

(a) The total energy of the system is given by:

where k is the force constant and A is the amplitude. By replacing we get:

= 72mJ

(b) we can get the speed by the conservation of energy (the kinetic energy and potential energy must equal the total energy in any place):

where we have used that x=1.15cm=0.0115m; A=6.00cm=0.06m

(c) Again, by the conservation of energy:

(d)

hope this helps!!

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