A 5.80 kg object on a horizontal frictionless surface is attached to a spring with spring constant 860 N/m. The object is displaced from equilibrium 50.0 cm horizontally and given an initial velocity of 9.9 m/s back toward the equilibrium position.

Question

A 5.80 kg object on a horizontal frictionless surface is attached to a spring with spring constant 860 N/m. The object is displaced from equilibrium 50.0 cm horizontally and given an initial velocity of 9.9 m/s back toward the equilibrium position.
(a) What is the frequency of the motion?
units in Hz

(b) What is the initial potential energy of the block-spring system?
units in J

(c) What is the initial kinetic energy?
units in J

(d) What is the amplitude of the motion?
units in m

drwls · Answer

(a) There is a standard formula for the frequency of spring/mass SHM.

f = [1/(2 pi)]*sqrt(k/M)

Use it.
(b) Ditto the P.E. of a stretched spring, (1/2) k X^2.

(c) (1/2) M Vo^2
(d) Amplitude X is whatever the P.E. is when K.E. = 0. That will happen when P.E. = total energy (b) + (c)