Spring's Highest Point and Spring Constant

Question

A mass of 0.500 kg is hung from a spring and allowed to come to rest. The mass is then pulled down 4 cm from this rest position and released from rest at t=0. The mass then oscillates with a period of 0.2 seconds. What is the value of y for the highest point reached by the mass, and find the time it took to reach that point. What is the spring constant of the spring. Show how you can use Newton's Laws to obtain the value of the spring constant k and give the value.

Thanks for any help! =)

Answer 1

Period v= 1/(2*pi) (k/m)^0.5=(1/2*pi)(k/(0.50)^0.5

0.2*(2*pi)=(k/0/5)^0.5

(0.2(2*pi))^2=k/0.5

(0.2(2*pi))^2*0.5=k

Spring constant

Potential energy of a spring is found from the equation;

U=1/2 k x^2

U=1/2 0.7896 (0.04)^2=6.317 E-4 J

Half of the journey the potential energy of the spring is changing to kinetic. The other half it is changing from kinetic back in to potential. Therefore the mass will be 8 cm higher when it reaches its peak. This if found in the laws of force and energy handed down by Newton.