Answer to Question #160919 in Classical Mechanics for Vanessa

Question

A 200g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0.250s. The total energy of the system is 2.00J. Find
(a) the force constant of tge spring
(b) the amplitude of the motion.

Answer 1

(a)

$$T=2\pi\sqrt{\dfrac{m}{k}},$$ $$k=\dfrac{4\pi^2m}{T^2},$$ $$k=\dfrac{4\pi^2\cdot0.2\ kg}{(0.25\ s)^2}=126.3\ \dfrac{N}{m}.$$

(b)

$$E=\dfrac{1}{2}kA^2,$$ $$A=\sqrt{\dfrac{2E}{k}},$$ $$A=\sqrt{\dfrac{2\cdot2.0\ J}{126.3\ \dfrac{N}{m}}}=0.177\ m.$$