Answer to Question #160921 in Classical Mechanics for wilder

Question

A 50.0 g object connected to a spring with a force constant of 35.0N/m oscillates with amplitude of 4.00cm on a frictionless, horizontal surface. Find
(a) the total energy of the system
(b) the speed of the object when its position is 1.00cm

Answer 1

(a) The total energy of the system can be found as follows:

$$E=\dfrac{1}{2}kA^2,$$ $$E=\dfrac{1}{2}\cdot35.0\ \dfrac{N}{m}\cdot(0.04\ m)^2=28\cdot10^{-3}\ J.$$

(b) The speed of the object can be found from the formula:

$$v=\sqrt{\dfrac{k}{m}(A^2-x^2)},$$ $$v=\sqrt{\dfrac{35.0\ \dfrac{N}{m}}{0.05\ kg}((0.04\ m)^2-(0.01\ m)^2)}=1.02\ \dfrac{m}{s}.$$