Question

A harmonic oscillator by attaching a mass of 2 kg to a spring with spring constant K= 200 N/M and allowed to oscillate with a maximum displacement of 4 cm. Determine the velocity of the mass when it is displaced x= 1 cm from the equilibrium position

Answer 1

given that

mass m = 2 kg

spring constant k = 200 N/m

maximum displacement A = 0.04 m

position x = 0.01 m

from the relation

total energy = kinetic energy +spring potential energy

1/2kA^2 = 1/2mv^2+1/2kx^2

2*v^2 = 200*0.04^2-200*0.01^2

v^2 = 0.15

v = 0.387 m/s