Question

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?

Answer 1

Answer:

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