A 0.480 kg object connected to a light spring with a spring constant of 18.0 N/m

Question

A 0.480 kg object connected to a light spring with a spring constant of 18.0 N/m oscillates on a frictionless horizontal surface.

a) Calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm.

E = J

vmax =  m/s

(b) What is the velocity of the object when the displacement is 2.00 cm?
± m/s

(c) Compute the kinetic and potential energies of the system when the displacement is 2.00 cm.

Now i just can't figure this one out!

For what values of x is the speed of the object 0.13 m/s?
x = ± cm

Explanation / Answer

For what values of x is the speed of the object 0.13 m/s? E = (1/2) k A^2 = 0.5*18*0.03*0.03 = 0.0081 J at any point we must have E=K+U E = K + U E = 0.5 k x^2 + 0.5 m v^2 0.0081 = 0.5 * 18.0 * x^2 + 0.5 * 0.480 * (0.13)^2 0.0081 = 9 * x^2 + 0.004056 >>>> x=2.12cm and x=-2.12cm

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