Considering a mass-spring system aligned horizontally moving at a velocity v.

Question

a) How will the velocity of the mass change if amplitude is doubled.

b) How will the velocity of the mass change if the spring constant is quartered?

I know the answer to the first one is that it will be doubled but am not 100% sure if that is correct. I am stuck on the second question.

Thank you.

Answer 1

the energy stored in the spring is
... ½ k x²
... this energy is K.E. when the spring is in the neutral position (the middle of its travel)

K.E. = ½ m v²
... so the velocity and the amplitude are directly related to each other (both squared)

a) velocity will double (as you thought)

b) quartering the spring constant (k)
will quarter the stored energy
... since energy is related to the square of the velocity
... quartering k will halve the velocity ... √¼ = ½