Question

A 0.500 kg block on a spring is pulled a distance of 0.200 m and released. The subsequent oscillations are measured to have a period 0.800 s. What is the spring constant and at what position is the block’s speed 1.00 m/s?

Answer 1

time period = 2pi*sqrt(m/k)

0.8 = 2pi*sqrt(0.5 / k)

k = 30.84 N/m

spring constant is 30.84 N/m

let the position at which block speed is 1m/s be x1

Energy at position x1 = energy at apmlitude

0.5mv^2 + 0.5kx1^2 = 0.5kx^2

0.5*1^2 + 30.84*x1^2 = 30.84*0.2^2

x1 = 0.154 m

so the position is 0.154 m