A mass m1 is hung from a spring oscillates on a spring with spring constant k1. The amplitude of its motion is A1 and it has a maximum magnitude acceleration a1. If the mass is doubled, the spring constant tripled, and the amplitude quadrupled, what will the new maximum magnitude acceleration be?

the new acceleration will be six times the initial acceleration

Explanation:

A mass m1 is hung from a spring oscillates on a spring with spring constant k1. The amplitude of its motion is A1 and it has a maximum magnitude acceleration a1. If the mass is doubled, the spring constant tripled, and the amplitude quadrupled, what will the new maximum magnitude acceleration be

mass = m1 acceleration

f=force applied

k=force constant

x=extension. amplitude or compression

a=

from hooke's law we know that the force exerted on an elastic material is directly proportional to the extension provided that the elastic limit is not exceeded

f=kx

m*a=k*x

a1=kx/m1

m2=2m1

k2=3k1

x2=4x1

substituing into the initial equation

a2=3k1*4x1/2m1

a2=6k1x1/m1

a2=6a1

the new acceleration will be six times the initial acceleration