Question

Tripling the displacement from equilibrium of an object in simple harmonic motion will change the magnitude of the object’s maximum acceleration by what factor?

Answer 1

In simple harmonic motion, the acceleration is directly proportional to the displacement. Therefore, tripling the displacement from equilibrium increases the maximum acceleration by a factor of nine.

Step-by-step explanation:

Tripling the displacement from equilibrium of an object in simple harmonic motion means that the maximum acceleration of the system will increase by a factor of nine. In simple harmonic motion, the acceleration at any point is given by a(t) = -k/m x(t), where k is the spring constant, and m is the mass of the object.

Because acceleration is directly proportional to displacement (x(t)), if you triple the displacement, the acceleration is tripled as well. However, since x(t) is squared in the formula for acceleration, tripling the displacement results in an increase by a factor of three squared, or nine.

Answer 2

a (max)= A (2pi/T)
a (max)= maximum acceleration
A= amplitude
T= periodic time

by definition, amplitude is the displacement from equillibrium point.

we see that maximum acceleration is directly proportional to the amplitude. so tripling the amplitude will triple the maximum acceleration.